<p>The numbers of integers between 1 and 10 6 have the sum …

Maths Permutations & Combination Definition of Combinations, Condition Combinations, Division into Groups, Derangements Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The numbers of integers between 1 and 10 6 have the sum of their digit equal to K(where 0 < K < 18) is -

(K + 6) C 6 – (K – 4) C 6

K C 6 – 6 · K C 4

K C 6 – 6 · K – 4 C 6

K + 6 C 6 – 6 · K – 4 C 6

Text Solution

Verified by Experts

The correct answer is:

The required no. of ways = no. of solution of the equation

(x 1 + x 2 + x 3 + x 4 + x 5 + x 6 = K)

Where 0 ≤ x i ≤ 9, i = 1, 2, …6, where 0 < K < 18

= Coefficient of x K in (1 + x + x 2 +….. + x 9 ) 6

= Coefficient of x K in

= Coefficient of x k in (1 – 6x 10 + 15 x 20 – ….)

(1 + 6 C 1 x + 7 C 2 x 2 + …. +(7 – K – 10 – 1) C K–10 x K–10 + ….+(7 + K – 1) C K x K + …)

= k + 6 C K – 6. K–4 C K–10

= k + 6 C 6 – 6. K–4 C 6 .

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