Swift .playground showing how to programmatically change the height of items in a stack view and track cells selected and unselected.

SelectingCollectionView.playground

//: Playground - noun: a place where people can play

import UIKit
import PlaygroundSupport

extension UIView {
    func asCircle(){
        self.layer.cornerRadius = self.frame.width / 2;
        self.layer.masksToBounds = true
    }
}


class MyCollectionViewCell: UICollectionViewCell {

    override func awakeFromNib() {
        print("awakeFromNib")
    }

    override init(frame: CGRect) {
        super.init(frame: frame)
        self.asCircle()
    }

    required init?(coder aDecoder: NSCoder) {
        fatalError("init(coder:) has not been implemented")
    }
    
     override var isHighlighted: Bool {
        didSet {
            if isHighlighted {
                UIView.animate(withDuration: 0.2, delay: 0, options: .curveEaseIn, animations: {
                    self.transform = CGAffineTransform(scaleX: 0.5, y: 0.7)
                }, completion: nil)
            } else {
                UIView.animate(withDuration: 0.2, delay: 0, options: .curveEaseOut, animations: {
                    self.transform = CGAffineTransform(scaleX: 1, y: 1)
                }, completion: nil)
            }
        }
    }

}
class MyViewController : UIViewController, UICollectionViewDelegateFlowLayout, UICollectionViewDelegate, UICollectionViewDataSource {

    // MARK: - Properties
    // views
    var headerView: UIView!
    var titleLabel: UILabel!
    var selView: UIView!
    var selLabel: UILabel!
    var collectionView: UICollectionView?

    // attributes
    var numberSelected = 0 // track this

    // MARK: - LifeCycle
    override func viewDidLoad() {
        super.viewDidLoad()

        setupHeader()
        setupCollection()
        setupSelection()
        setupStack()
    }


    // MARK: Methods
    func updateSelectedCount(_ upOrDown:String) {
        switch(upOrDown) {
        case "up":
            numberSelected += 1
        case "down":
            if numberSelected > 0 {
                numberSelected -= 1
            }
        default:
            print("not up or down")
        }
    }

    // MARK: CollectionView Methods

    func collectionView(_ collectionView: UICollectionView, numberOfItemsInSection section: Int) -> Int {
        return 40
    }

    func collectionView(_ collectionView: UICollectionView, layout collectionViewLayout: UICollectionViewLayout, sizeForItemAt indexPath: IndexPath) -> CGSize {
        return CGSize(width: 50.0, height: 50.0)
    }

    func collectionView(_ collectionView: UICollectionView, cellForItemAt indexPath: IndexPath) -> UICollectionViewCell {
        let cell = collectionView.dequeueReusableCell(withReuseIdentifier: "MyCell", for: indexPath) as! MyCollectionViewCell
        cell.backgroundColor = .black
        return cell
    }

    func collectionView(_ collectionView: UICollectionView, didSelectItemAt indexPath: IndexPath) {
        let selectedCell = collectionView.cellForItem(at: indexPath)
        selectedCell?.backgroundColor = .blue
        updateSelectedCount("up")
        let selected = String(describing: indexPath.row + 1)
        let selString = "You selected \(selected) for a total of \(numberSelected)"
        selLabel.text = selString
    }

    func collectionView(_ collectionView: UICollectionView, didDeselectItemAt indexPath: IndexPath) {
        let deselectedCell = collectionView.cellForItem(at: indexPath)
        deselectedCell?.backgroundColor = .gray
        updateSelectedCount("down")
        let deselected = String(describing: indexPath.row + 1)
        let selString = "You deselected \(deselected) for a total of \(numberSelected)"
        selLabel.text = selString
    }



    // MARK: SetUp Methods

    func setupHeader() {
        headerView = UIView()
        headerView.backgroundColor = .white

        titleLabel = UILabel()
        titleLabel.text = "Update"
        titleLabel.textAlignment = .center
        titleLabel.font = UIFont(name: titleLabel.font.fontName, size: 20)
        headerView.addSubview(titleLabel)

        titleLabel.translatesAutoresizingMaskIntoConstraints = false
        titleLabel.centerXAnchor.constraint(equalTo: headerView.centerXAnchor).isActive = true
        titleLabel.centerYAnchor.constraint(equalTo: headerView.centerYAnchor).isActive = true
    }

    func setupCollection() {
        let frame = self.view.frame
        let layout = UICollectionViewFlowLayout()
        collectionView = UICollectionView(frame: frame, collectionViewLayout: layout)
        collectionView?.delegate = self
        collectionView?.dataSource = self
        self.collectionView?.backgroundColor = .white
        self.collectionView?.register(MyCollectionViewCell.self, forCellWithReuseIdentifier: "MyCell")
        collectionView?.allowsMultipleSelection = true
    }

    func setupSelection() {
        selView = UIView()
        selView.backgroundColor = .white

        selLabel = UILabel()
        selLabel.text = ""
        selLabel.numberOfLines = 0
        selLabel.lineBreakMode = .byWordWrapping
        selLabel.textAlignment = .center
        selLabel.font = UIFont(name: selLabel.font.fontName, size: 14)
        selView.addSubview(selLabel)

        selLabel.translatesAutoresizingMaskIntoConstraints = false
        selLabel.centerXAnchor.constraint(equalTo: selView.centerXAnchor).isActive = true
        selLabel.centerYAnchor.constraint(equalTo: selView.centerYAnchor).isActive = true
        selLabel.widthAnchor.constraint(equalTo: selView.widthAnchor).isActive = true
    }


    func setupStack() {
        let stackView = UIStackView(arrangedSubviews: [headerView, collectionView!, selView])
        stackView.axis = .vertical
        stackView.distribution = .fill
        stackView.alignment = .fill
        stackView.spacing = 10
        stackView.translatesAutoresizingMaskIntoConstraints = false

        // add some component constraints
        let headHeight = headerView.heightAnchor.constraint(equalToConstant: 50)
        let selHeight = selView.heightAnchor.constraint(equalToConstant: 50)
        stackView.addConstraints([headHeight, selHeight])

        view.addSubview(stackView)

        //autolayout the stack view
        let sH = NSLayoutConstraint.constraints(withVisualFormat: "H:|-20-[stackView]-20-|", options: NSLayoutFormatOptions(rawValue: 0), metrics: nil, views: ["stackView":stackView])
        let sV = NSLayoutConstraint.constraints(withVisualFormat: "V:|-30-[stackView]-30-|", options: NSLayoutFormatOptions(rawValue:0), metrics: nil, views: ["stackView":stackView])
        view.addConstraints(sH)
        view.addConstraints(sV)
    }
}

PlaygroundPage.current.liveView = MyViewController()

This is how it looks:

updated to add little spring animation on selection and deselection and to change "picked" to "selected" and "deselected" so that it is clear to users.