Question

The value of 5C4 × 4C2 is

Answer 1

Answer:

We know that,

n

C

r

+

n

C

r−1

=

n+1

C

r

Since,

⇒

10

C

4

+

9

C

4

+

8

C

4

+

7

C

4

+

6

C

4

+

5

C

4

+

5

C

5

−1

⇒

10

C

4

+

9

C

4

+

8

C

4

+

7

C

4

+

6

C

4

+

6

C

5

−1

⇒

11

C

5

−1

Answer 2

Value of ⁵C₄ × ⁴C₂ is  30

Given:

• ⁵C₄ × ⁴C₂

To Find:

• Value

Solution:

• $^{n}C_{r}=\dfrac{n!}{r!(n-r)!}$
• n! = Product of natural numbers from 1 to n

Step 1:

Calculate ⁵C₄

= 5!/(4!(5 - 4)!)

= 5!/(1!4!)

= 5 × 4! /(1 × 4!)

= 5

Step 2:

Calculate  ⁴C₂

= 4!/(2!(4 - 2)!)

= 4!/(2!2!)

=4 × 3 × 2! /((2!2!))

= 12/2!

= 12/2

= 6

Step 3:

Calculate the product Substituting ⁵C₄ = 5 and ⁴C₂ = 6

⁵C₄ × ⁴C₂ = 5 × 6  = 30

Hence, Value of ⁵C₄ × ⁴C₂ is  30