Permutations and Combinations 1 Question 4

4. The number of seven-digit integers, with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only, is

(2009)

(a) 55

(b) 66

(c) 77

(d) 88

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Answer:

Correct Answer: 4. (c)

Solution:

  1. There are two possible cases

Case I Five 1’s, one 2’s, one 3’s

Number of numbers $=\frac{7 !}{5 !}=42$

Case II Four 1’s, three 2’s

Number of numbers $=\frac{7 !}{4 ! 3 !}=35$

$\therefore$ Total number of numbers $=42+35=77$



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