7 freshmen, 9 sophomores, 8 juniors, and 8 seniors are eligible to be on a committee. In how many ways can a dance committee of 14 students be chosen? In how many ways can a dance committee be chosen if it is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors.

Step-by-step explanation:

Given

Total:

Selection

Required

Determine the number of selection

To do this, we make use of combination formula:

For Freshmen, we have:

For Sophomores, we have:

For Juniors, we have:

For Seniors

and implies *, so we have:

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)