Question

True or False

1.The number of permutations of r objects out of n (r > 1), is greater than the number of combinations of r objects out of n.

Answer 1

True

Explanation:

Permutation is act of arranging members of a set while combination is selection of the items from collection.

The number of permutation of r object out of n is:

`^nP_r=\frac {n!}{(n-r)!}`

The number of combinations of r object out of n is:

`^nC_r=\frac {n!}{(n-r)!* r!}`

Or,

`^nC_r=\frac {^nP_r}{r!}`

So, number of the permutations of r objects out of n is greater than number of the combinations of r objects out of n.