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Compute The Following. (A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9

Sagot :

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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

What is Permutations and Combination ?

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:

https://brainly.com/question/28065038

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