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:
- 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 $=42+35=77$
