Q. 24.7( 6 Votes )

# Prove that ^{9}P_{3} + 3 × ^{9}P_{2} = ^{10}P_{3}.

Answer :

To Prove: ^{9}P_{3} + 3 × ^{9}P_{2} = ^{10}P_{3}

Formula Used:

Total number of ways in which n objects can be arranged in r places (Such that no object is replaced) is given by,

^{n}P_{r}

The equation given below needs to be proved i.e

^{9}P_{3} + 3 × ^{9}P_{2} = ^{10}P_{3}.

+

(9 × 8 × 7) + (3 × 9 × 8) = 10 × 9 × 8

10 × 9 × 8 = 10 × 9 × 8

Hence, proved.

^{9}P_{3} + 3 × ^{9}P_{2} = ^{10}P_{3}.

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Which of the following are true :

(2 + 3)! = 2! + 3!

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