Question

How many different selections can be made by taking four of the digits $3,4,7,5,8,1$? How many different numbers can be formed with four of these digits?

Answer 1

Total digits are $6$.

(1) Number of ways of selecting $4$ digits out of $6$ digits is given by $={}^6{C}_4=\frac{6!}{4!2!}=\frac{6\times 5}{2}=15$.

(2) Selected $4$ digits can be arranged in $4$ places to get different numbers i.e. $={}^6{C}_4\times 4!=15\times 24=360$.