Question

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

Answer 1

There are two possible cases.Case I:Five 1's one 2's one 3'sNumber of numbers =7!5!7!5!⇒7×6×5!5!⇒7×6×5!5!=42=42Case II: Four 1's three 2'sNumber of numbers =7!4!3!7!4!3!⇒7×6×5×4!4!×3×2⇒7×6×5×4!4!×3×2=35=35Total number of numbers =42+35=77
Hence 77 is the answer.
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