Question

Find n if
$\rm ^{7}P_{3}=n. ^{7}C_{3}$

Answer 1

Answer:

6

Step-by-step explanation:

Hi,

Given ⁷P₃ = n.⁷C₃

We know that ⁿPₓ = n!/(n-x)!

ⁿCₓ = n!/(n-x)!x!

ⁿPₓ/ⁿCₓ = x!

Thus, ⁷P₃ /⁷C₃ = 3! = n

⇒ n = 3! = 6

Thus, the value of n is 6.

Hope, it helps !

Answer 2

Answer:

The value of n = 6

Step-by-step explanation:

We know the formula of Permutation and Combination as shown below:-

nPr = n! / (n - r)!

nCr = n! / r! (n - r)!

Therefore,

7P3 = 7! / (7 - 3)! = 7! / 4! = (7 * 6 * 5 * 4!) / 4! = 7 * 6 * 5 = 210.

7C3 = 7! / 3! * (7 - 3)! = 7! / (3! * 4!) = (7 * 6 * 5)/3! = 35.

Therefore,

7P3 = 6 * 7C3 (comparing it with the expression given in the question we get)

or, n = 6 [Ans]