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8. Permutations
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Q12 of 140 Page 267

Evaluate , when n = 15 and r = 12.

Given : n = 15 and r = 12


To Find : Value of at given n and r


Formula :


•


•


Let ,



Substituting n = 15 and r = 12 in above equation,




By using above formula,



Cancelling (12!) from numerator & denominator,



∴x = 455


Conclusion : Value of at n = 15 and r = 12 is 6.


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10

If = 2 : 1, find the value of n.

11

If = 44 : 3, find the value of n.

13

Prove that (n + 2) × (n!) + (n + 1) ! = (n!). (2n + 3)

14

Prove that

(i) = n(n – 1) (n – 2) …. (r + 1)


(ii) (n – r + 1).


(iii)


Questions · 140
8. Permutations
1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1 1 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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