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Question

The number of 7-digit numbers formed by the digits 1, 2 and 3 only whose sum of the digits equals 10, is

A
42
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B
55
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C
77
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D
35
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Solution

The correct option is C 77
Let 1 appear x times, 2 appear y times and 3 appear z times.
Then, x+y+z=7 and x+2y+3z=10
Solving above equations, we get
y+2z=3
Possible values are
y=1,z=1 and x=5
or y=3,z=0 and x=4
Total count =7!5! 1! 1!+7!4! 0! 3!=77

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