Which expression is equivalent to ^3 sqrt x^5y

a.) 20 ways

b.) 12 ways

c.) 10 ways

d.) 4 ways

Step-by-step explanation:

This question deals with selection of a few from a general larger possible options and the combination formula for selection is used to solve this question. This combination formula is denoted by:

nCr = n!/(n-r)! × r!

a.) to select the people to fill the 3 positions from the possible 6 options, Number of ways become: 6C3 = 6!/(6-3)! × 3! = 20Ways

b.) If Alice or Ben must be the chair person, then we have two possibilities.

If Alice is Chairperson, then we chose other 2 positions from the remaining 4 members or Ben be the chairperson and we choose the remaining 2 positions from the 4 members left. Number of ways of this becomes:

number of ways to choose chairperson × number of ways to choose other two posts = 2C1 × 4C2 = 12ways.

c.) If Egbert must hold one of the offices, then we have just 2 positions left to be chosen from 5 member. Number of ways for this = 5C2 = 10ways

d.) If Dolph and Francisce must hold office then the last office is to be given to Just 1 among the 4 possible members. Number of ways for this = 4C1 = 4ways.