The coefficient of `x^2y^3` in the expansion of `(1-x+y)^(20)` is `(20 !)/(213 !)` b. `-(20 !)/(213 !)` c. `(20 !)/(5!2!3!)` d. none of these

Question

The coefficient of `x^2y^3` in the expansion of `(1-x+y)^(20)` is `(20 !)/(213 !)` b. `-(20 !)/(213 !)` c. `(20 !)/(5!2!3!)` d. none of these

The coefficient of `x^2y^3` in the expansion of `(1-x+y)^(20)` is `(20 !)/(213 !)` b. `-(20 !)/(213 !)` c. `(20 !)/(5!2!3!)` d. none of these
A. `(20!)/(2!3!)`
B. `-(20!)/(2!3!)`
C. `(20!)/(5!2!3!)`
D. `(20!)/(15!2!3!)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - D
The general term in the expansion of `(1-x+y)^(20)` is
`(20!)/(r!s!t!)1^(r)(-x)^(s)(y)^(t)`, where `r+s+t=20`
For `x^(2)y^(3)`, we have the term
`(20!)/(15!2!3!) 1^(15)(-x)^(2)(y)^(3)`
Hence, the coefficient of `x^(2)y^(3)` is
`(20!)/(15!2!3!)`

4 views Answered 2023-02-05 15:29