Answer to Question #128489 in Statistics and Probability for ysabe castro

Question

a In how many different ways can it select a group of 4 members?




b In how many different ways can it elect a president, vice-president, secretary and treasurer? One member CANNOT hold more than one job. (optional)

Answer 1

Solution:

a) Here n is not mentioned.so let us take n= 10 for example

You have a total of 10 people to choose from. Of these 10 people you are supposed to create a group of 4. Since order is not important here we use combination.

Formula:

nC_r= $\frac{n!}{(n-r)!r!}$

Hence 10C₄= $\frac{10!}{(10-4)!4!}$

=$\frac{10!}{(6)!4!}$

= 210

Hence different ways to select a group of 4 members = 210

b)different ways can it elect a president, vice-president, secretary and treasurer= 10*9*8*7= 5040 ways