Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the numbers in P are formed by using the digits 1,2 and 3 only, then the number of elements in the set $P$ is :

Question

Aicharya · Accepted Answer

(i) number of numbers created using
$1111133=\frac{7!}{5!2!} \Rightarrow 21$
(ii) number of numbers created using
$1111223=\frac{7!}{4!2!} \Rightarrow 105$
(iii) number of numbers created using
$1112222=\frac{7!}{4!3!} \Rightarrow 35$
Total $=161$ .

Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the numbers in P are…

Solution