Question

The number of seven digit integer is to be formed using only 1, 2 &3 such that the sum of all the digits is 10 . so how many such seven digit number is possible ?

Answer 1

Answer:

Step-by-step explanation:

There are only two integer partitions of 10 of length 7 formed from the digits 1,2,3: {3,2,1,1,1,1,1} and {2,2,2,1,1,1,1}. The number of ways you can form numbers from the first set can be computed using a multinomial:

7!1!1!5!=42

and for the second set is

7!3!4!=35

so the total is 77.