Question

Two players take turns writing X and O in a 3-by-3 grid until all the cells are full. The first player chooses whether to use X's or O's. How many ways are there to fill all the cells with Xs and Os?

9!

252

126

2^9

What is the number of ways to seat 3 boys and 2 girls in a row if each boy must sit next to at least one girl?

36

184

148

48

How many ways can 2 pennies, 3 nickels, and 5 quarters be arranged in a row?

30

10!

5040

2520

Answer 1