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\(\sum _{k=0}^{6}{}^{51-k}C_{3}\) is equal to [JEE Main 2023, 25 Jan (Shift 2)]

Q1

\(\sum _{k=0}^{6}{}^{51-k}C_{3}\) is equal to

[JEE Main 2023, 25 Jan (Shift 2)]

a

\({}^{51}C_{4}-{}^{45}C_{4}\)

b

\({}^{51}C_{3}-{}^{45}C_{3}\)

c

\({}^{52}C_{4}-{}^{45}C_{4}\)

d

\({}^{52}C_{3}-{}^{45}C_{3}\)

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