We know that the formula for permutations for n objects taken r at a time is

P(n, r) = n! / (n - r)!.Since for each combination of r objects selected at random from a group of n objects, the number of permutations is r!, therefore the total number of permutations is r! times the total number of combinations.

Now let the total number of combinations of n objects taken r at a time be x. By the above derivation,

x * r! = P(n, r)That is,

x * r! = n! / (n - r)!Therefore,

x = n! / r!(n - r)!Therefore the total number of combinations of n objects taken r at a time is

C(n, r) = n! / r!(n - r)!

## No comments:

## Post a Comment