The Computation results of given combination and permutation expression,
(A) P(9, 3) = 504
(B) C(9, 3) = 84
(C) P(8,8) = 40,320
(D)P(9,9) = 1
A permutation is an arrangment of arranging objects or numbers in order.
The formula for permutations is
ⁿPᵣ = n!/(n-r)!
Combinations are the way of selecting objects or numbers from a group of objects, in such a way that the order of the objects does not matter.
The formula for combinations is,
ⁿCᵣ = n!/[r! (n-r)!]
ⁿCᵣ represents the number of combinations from “n” objects taken “r” at a time.
We have given some expressions and we shall compute these.
(A) P(9, 3) , here n = 9 and r = 3
=> P(9, 3) = 9!/(9-3)! = 9!/6! = 9×8×7×6!/6!
P(9, 3) = 9×8×7 = 504
(B) C(9, 3) = 9!/3!(9-3)! = 9!/6!×3!
= 9×8×7×6!/6!(3×2×1) = 9×8×7/6 = 84
(C) P(8, 8) = 8!/(8-8)!
= 8!/0! = 8! = 8×7×6×5×4×3×2×1 = 40,320
(D) C (9, 9) = 9!/9!(9-9)!
= 9!/9! 0! = 1
Hence ,we get all the values of given expression.
To learn more about Combination and permutation, refer:
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