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

The number of seven digit integers, with sum of the dig... | Permutations and Combinations (Mathematics)

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(1) The digits used are

1,1,1,1,1,2,3

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The number of numbers formed

=\frac{\lfloor7}{\lfloor{5}}=42 \\

(2) The digits used are

1,1,1,1,2,2,2 \\

The number of numbers formed

=\frac{\lfloor7}{\lfloor4 \lfloor3}=\frac{7.6 \cdot 5}{6}=35 \\

The total number of numbers

=42+35=77