Decide if the situation involves permutations, combinations, or neither. Explain

Question

Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways a four-member committee can be chosen from 10 people. Does the situation involve permutations, combinations, or neither? Choose the correct answer below. A. Neither. A line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects. B. Combination. The order of the committee members does not matter. C. Permutation. The order of the committee members matters.

Explanation / Answer

Solution:

The number of ways a four member commitee can be chosen from 10 people
Here we are intrested in finding the ways of selecting a four member in commitee from 10 people

as we can not select same person in a commitee Or commitee must have different people AND order of selection of people in a commitee is not matter

So consider following steps to form a commitee of four member
I] select 1st member from 10 people in 10C1=10 ways

II]Now as we find 1st member, we find 2nd member from remaining people (i.e. 9 people ) in 9C1=9 ways
  
III]Now as we find 1st and 2nd member, we find 3rd member from remaining people (i.e. 8 people ) in 8C1=8 ways

IV] Now as we find 1st , 2nd and 3rd member, we find 4th member from remaining people (i.e. 7 people ) in 7C1=7 ways

Now Commitee can be form in 10C1 + 9C1 + 8C1 + 7C1=34 numbers of ways

Hence the answer is B. Combination . the Oreder of the commitee members does not matters.

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