Question

There are 110 applicants for three cosmetology positions. How many different ways can the three positions be filled? Select one: 215,820 ways 3 ways 1,294,920 ways 1,331,000 ways

Answer 1

Answer: 215,820 ways

Explanation:

There are 110 applicants for three cosmetology positions. How many different ways can the three positions be filled?

Number of positions = 110

Number of applicants = 3

Number of way in which the positions can be filled ;

This is a combination problem

nCr = n! ÷ (n-r)! r!

110C3 = 110! ÷ (110 - 3)! 3!

110C3 = 110! ÷ 107! 3!

110C3 = (110 * 109 * 108) / (3 * 2 * 1)

110C3 = 1294920 / 6

= 215820 ways