Answer:252 committees
Step-by-step explanation: This is a question of permutation and combinations.
Let us first know what permutations and combinations.
A number of permutations (order matters) of n things taken r at a time:
nPr=n!(n−r)!
A number of combinations (order does not matter) of n things taken r at a time:
nCr=n!(n−r)!r!
So, in this question, we have to find that in how many ways, we can select a committee of five members from a group of 10 people.
So, in this question, the process of choosing the persons does not matter which means the order of choice does not matter.
So, we are going to use the formula for this question is nCr=n!(n−r)!r!
We are choosing 5 persons from 10 persons where order does not matter.
Then, the numbers of ways are 10!(10−5)!5!
As we know that n!=n×(n−1)×(n−2)×(n−3)×........×2×1
Then, 10!(10−5)!5!
can be written as
10!(10−5)!5!=10!5!×5!=10×9×8×7×6×5×4×3×2×1(5×4×3×2×1)×(5×4×3×2×1)
Which is also can be written as
10!(10−5)!5!=10×9×8×7×65×4×3×2×1=105×9×84×7×63×2=2×9×2×7×1=252
Hence, 10!(10−5)!5!=252
Therefore, the number of ways of selecting a committee of 5 members from a group of 10 persons is 252.