Q2 of 140 Page 288

Prove that 9P3 + 3 × 9P2 = 10P3.

To Prove: 9P3 + 3 × 9P2 = 10P3


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,


nPr


The equation given below needs to be proved i.e


9P3 + 3 × 9P2 = 10P3.


+


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


10 × 9 × 8 = 10 × 9 × 8


Hence, proved.


9P3 + 3 × 9P2 = 10P3.


More from this chapter

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1

Evaluate:

6P6


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Evaluate:

9P0


 3

(i) If nP5 = 20 × nP3, find n.

(ii) If 16 × nP3 = 13 × n+1P3, find n.


(iii) If 2nP3 = 100 × nP2, find n.


 4

(i) If If 5Pr = 2 × 6Pr–1, find r.

(ii) If 20Pr = 13 × 20Pr–1, find r.


(iii) If 11Pr = 12Pr–1, find r.