JEE MAIN - Mathematics (2025 - 29th January Morning Shift - No. 2)
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 :
164
158
161
173
Explanation
(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
$$\begin{aligned} & 1112222=\frac{7!}{4!3!} \Rightarrow 35 \\ & \text { Total }=161 \end{aligned}$$
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