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Solution


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 :          [2025]
1 158  
2 164  
3 173  
4 161  

Ans.

(4)

(i) Number of numbers formed using 1 and 3, i.e.,

     =7!5!2!=21

(ii) Number of numbers formed using 1, 2, 3 i.e.,

       =7!4!2!=105

(iii) Number of numbers formed using 1 and 2, i.e.,

       =7!3!4!=35

Number of elements in set P = 161.