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 :

(1) 158

(2) 173

(3) 164

(4) 161

Answer 1

Correct option is (4) 161  

(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