# Thread: Counting Principles, ways to pick apple or pear and then pick apple and pear

1. ## Counting Principles, ways to pick apple or pear and then pick apple and pear

There are 15 different apples and 10 different pears. How many ways are there for Jack to pick an apple or a pear and then for Jill to pick an apple and a pear?

The answer is 15 * 10 * (14 + 9)

I first looked at Jack:
Ways to pick an apple or pear
15+10 ? He can pick one out of 25 to get an apple or a pear...

the Jill, needs to pick an apple and a pear:
I do not understan how to start here...

I think, they are 2 events which are dependent, so you would multipy the results.

Thanks for any hints!

2. Originally Posted by DBA
There are 15 different apples and 10 different pears. How many ways are there for Jack to pick an apple or a pear and then for Jill to pick an apple and a pear?

The answer is 15 * 10 * (14 + 9)

I first looked at Jack:
Ways to pick an apple or pear
15+10 ? He can pick one out of 25 to get an apple or a pear...

the Jill, needs to pick an apple and a pear:
I do not understan how to start here...

I think, they are 2 events which are dependent, so you would multipy the results.

Thanks for any hints!
Split it into two cases.... (i) Jack picks an apple.... (ii) Jack picks a pear

Jack picks an apple and .........Jill picks an apple and a pear in 15(14)10 ways.

How many ways can Jack pick a pear and........ Jill picks an apple and a pear ?