TS EAMCET · Maths · Permutation Combination
The number of integers lying between 1000 and 10000 such that the sum of all the digits in each of those numbers becomes 30 is
- A \(84\)
- B \(96\)
- C \(45\)
- D \(75\)
Answer & Solution
Correct Answer
(A) \(84\)
Step-by-step Solution
Detailed explanation
Let the 4-digit number be \( d_1 d_2 d_3 d_4 \). The sum of digits is \( d_1 + d_2 + d_3 + d_4 = 30 \). Constraints: \( 1 \le d_1 \le 9 \), \( 0 \le d_2, d_3, d_4 \le 9 \). Let \( x_1 = d_1 - 1 \). Then \( 0 \le x_1 \le 8 \). Equation becomes \( x_1 + d_2 + d_3 + d_4 = 29 \).…
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