Muhammad's pennies

Probability Level 2

Jenny places $100$ pennies on a table, with $30$ showing heads and $70$ showing tails. She chooses $40$ distinct pennies uniformly at random and turns them over. That is, if a chosen penny was showing heads, she turns it to show tails; if a chosen penny was showing tails, she turns it to show heads. After this process, what is the expected number of pennies showing heads?

This problem is shared by Muhammad A.