In how many ways can the 10 children be selected

The Hewitt Elementary School PTA plans to use students in their next program. They want 5 children from MRs. Perry's PE class to give a PE activity demonstration; 2 children from MRs. Brown's class, a boy and a girl, to hand out programs; and 3 children from Ms. Gilchrest's class: 1 to give the welcome, 1 to lead in the pledge to the flag, and 1 to tell about the science fair. Mrs. Perry has 15 children in her PE class, Mrs. Brown has 9 boys and 13 girls in her class, and Ms. Gilchrest has 17 children in her class. In how many ways can the 10 children be selected?

Just write it out and multiply everything together:

They want
5 children from Mrs. Perry's PE class to give a PE activity demonstration;
2 children from Mrs. Brown's class, a boy and a girl, to hand out programs;
3 children from Ms. Gilchrest's class:
1 to give the welcome, 1 to lead in the pledge to the flag, and 1 to tell about the science fair.

Mrs. Perry has 15 children in her PE class,
Mrs. Brown has 9 boys and 13 girls in her class,
and Ms. Gilchrest has 17 children in her class.

In how many ways can the 10 children be selected?
15 choose 5 *
9 choose 1 * 13 choose 1 *
17 * 16 * 15 [ since these last three are performing different tasks ]

15 choose 5 = 3003
* 9 * 13 *
17 * 16 * 15 = 1,433,512,080 ← Answer