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Q.

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 :

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a

173

b

161

c

158

d

164

answer is D.

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Detailed Solution

(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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