Question

Without calculating the numbers, determine which of the following is greater. Explain.

(a) The number of combinations of 10 elements taken six at a time
(b) The number of permutations of 10 elements taken six at a time

Answer 1

the number of combinations is always less than the number of permutations

Explanation:

Without considering numbers , the number of combinations is always less than the number of permutations since the permutations consider the different arrangements of the elements for given set of numbers taken as different permutations, while the combination only takes one arrangement for any given set of numbers taken.

Mathematically

permutations of 10 elements taken six at a time= A( 10 ,6) = 10!/6!

combinations of 10 elements taken six at a time = C ( 10 ,6) = 10!/[6! * (10-6)!] = 10!/[ 6! * 4! ] = A/4!

since 4!>1 then C<A