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IPMAT Indore 2024 - QA (MCQ) Q35 Explanation
November 26, 2024
Explanation:
(a) Given 𝑥1+𝑥2+𝑥3+𝑥4 = 50 …(i) and 𝑥1 ≥ 1 or 𝑥1 − 1 ≥ 0 | 𝑥2 ≥ 2 or 𝑥2 − 2 ≥ 0 | 𝑥 3 ≥ 0 | 𝑥4 ≥ 0
Let 𝑥1 − 1 = a | 𝑥2−2 = b | 𝑥3 = c | 𝑥4 = d
So, now we have a, b, c, d ≥ 0
Equation (i) can be written as (a+1) + (b+2) + c + d = 50
or, a + b + c + d = 47
We have to find non-negative integer solution of above equation.
It can be find be find out using the formula 𝑛+𝑟−1 C 𝑟−1 where, n = 47 & r = 4
∴ Total number of solutions = 47+4−1 C 4−1 = 50 C 3 = 50×49×48/3×2×1
= 19600 Ans.