Question

Question 1)
What is the value of Permutation P(6,1)+P(9,3)
А
120
o
B
310
o
C
510​

Answer 1

The value of P(6,1) + P(9,3) = 510

Given :

The expression P(6,1) + P(9,3)

To find :

The value of the expression

A. 120

B. 310

C. 510

Formula :

$\displaystyle \sf{ P(n,r)} = {}^{n}P_r= \frac{n!}{(n - r)!}$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is P(6,1) + P(9,3)

Step 2 of 2 :

Find the value of the expression

P(6,1) + P(9,3)

$\displaystyle \sf{ = {}^{6}P_1 + {}^{9}P_3 }$

$\displaystyle \sf{ = \frac{6!}{(6 - 1)!} + \frac{9!}{(9 - 3)!} }$

$\displaystyle \sf{ = \frac{6!}{5!} + \frac{9!}{6!} }$

$\displaystyle \sf{ = \frac{6 \times 5!}{5!} + \frac{9 \times 8 \times 7 \times 6!}{6!} }$

$\displaystyle \sf{ = 6 + (9 \times 8 \times 7) }$

$\displaystyle \sf{ = 6 +504}$

$\displaystyle \sf{ = 510}$

Hence the correct option is C. 510