The value of ^50C_4 + _r=1^6 ^56-rC_3 is: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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The value of^{50} C_{4} + \sum_{r = 1}^{6}^{56 - r} C_{3} is:

Solution & Step-by-step Explanation

The sum is S =^{50} C_{4} + (^{55} C_{3} +^{54} C_{3} +^{53} C_{3} +^{52} C_{3} +^{51} C_{3} +^{50} C_{3}) .Rearranging: S = (^{50} C_{4} +^{50} C_{3}) +^{51} C_{3} +^{52} C_{3} +^{53} C_{3} +^{54} C_{3} +^{55} C_{3} Using the identity^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r} : S = (^{51} C_{4} +^{51} C_{3}) +^{52} C_{3} +^{53} C_{3} +^{54} C_{3} +^{55} C_{3} S = (^{52} C_{4} +^{52} C_{3}) +^{53} C_{3} +^{54} C_{3} +^{55} C_{3} S =^{53} C_{4} +^{53} C_{3} +^{54} C_{3} +^{55} C_{3} S =^{54} C_{4} +^{54} C_{3} +^{55} C_{3} S =^{55} C_{4} +^{55} C_{3} S =^{56} C_{4}

Try it yourself before checking the explanation above.

The value of^{50} C_{4} + \sum_{r = 1}^{6}^{56 - r} C_{3} is:

^{55} C_{4}

^{55} C_{3}

^{56} C_{3}

^{56} C_{4}

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