If the number of combinations of n different things taken (r+r) at a time be equal to the number of combinations taken (r-r) at a time , find the value of n.

(i) If the number of permutations of n different thing taken r at a time be denoted by (nPr) Show that,

Show that in the number of combinations of 2n different things taken n at a time , the number of combinations in which a particular thing occurs , is equal to the number in which it does not occur .

What is the total number of combination of n different things taken 1, 2, 3,...,n at a time ?

The number of combinations of n different things taken r at a time in which p particular things always occur is -

The number of permutations of n different things taken r at a time in which 4 particular things never occur is -

If six times the number of permutations of n things taken 3 at a time is equal to seven times the number of permutations of (n-1) things chosen 3 at a time, find n.