JEE Mains · Maths · STD 11 - 6. permutation and combination
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 :
- A 173
- B 164
- C 158
- D 161
Answer & Solution
Correct Answer
(D) 161
Step-by-step Solution
Detailed 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 \(1112222=\frac{7!}{4!3!} \Rightarrow 35\) Total \(=161\)
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