Question

A cheerleading squad consists of ten cheerleaders of ten different heights. How many ways are there for the cheerleaders to line up for a photo in two rows of five people each so that each cheerleader in the back row is taller than the one immediately in front?

Answer 1

11340

Explanation:

We have 10 cheerleaders of ten different heights. There are two rows each having 5 positions so that five cheerleaders occupy the first row that have height less than the five cheerleaders who occupied the second row.

Therefore, Out of ten cheerleaders, two cheerleaders will be selected out of which the tallest one will occupy the position in the upper row and the second one will occupy in the lower row, therefore these two positions will be occupied in
`10C_(2)` ways. Now, we are left with 8 cheerleaders and following the same path, the next two positions will also be occupied in
`8C_(2)`ways, similarly, following the same path, the number of ways the cheerleaders will occupy the position will be:
`10C_(2)`×
`8C_(2)`×
`6C_(2)`×
`4C_(2)`×
`2C_(2)`

=11340