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

Question

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 :

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

$$\begin{aligned}
& 1112222=\frac{7!}{4!3!} \Rightarrow 35 \
& \text { Total }=161
\end{aligned}$$

Solutions · 1