QJEEM21Maa197: JEE Main 2021 Mathematics - Class 11 JEEM21Maa197 Solution: If , then is equal to ______________.

Question

Verified Solution • 2025–26 Session moderate

If

{}^1{P_1} + 2.{}^2{P_2} + 3.{}^3{P_3} + .... + 15.{}^{15}{P_{15}} = {}^q{P_r} - s,0 \le s \le 1

, then

{}^{q + s}{C_{r - s}}

is equal to ______________.

Accepted Answer

{}^1{P_1} + 2.{}^2{P_2} + 3.{}^3{P_3} + .... + 15.{}^{15}{P_{15}}

= 1! + 2 . 2! + 3 . 3! + ..... 15

\times

15!

= \sum\limits_{r = 1}^{15} {(r + 1)! - (r)!}

= 16!

-

1

=

{}^{16}{P_{16}}

-

1

\Rightarrow

q = r = 16, s = 1

{}^{q + s}{C_{r - s}} = {}^{17}{C_{15}}

= 136

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