Question

There are 100 members in the U.S. Senate. Consider the following two selection processes.

1. Two members are to be randomly selected to work together as a special investigative committee.
2. Two members are to be randomly selected with the first being the president of a special investigative committee and the second being the vice president of that committee.

Which selection process would utilize permutations to find the number of outcomes? Why? How many permutations would there be?

Answer 1

The second selection process would utilize permutations to find the number of outcomes . That is in which first being president and second being vice president .

It's because in the second selection the order of selection is considered .If we select A first means A is president and select B secondly then B is vice President.If we select same A and B in a reverse order then it is an another selection because the president and vice president is changed . Hence the second selection need permutation method.

In the first selection order never matters hence AB and BA is same selection hence it is obtained by combination.  

Number of permutations is given as ,

2 members are permutated among the group of 100 hence answer is ,

Answer = N P _k

=

N = 100

K = 2

  Answer = 100 P₂

​ =

=

= 9900