Question

If nC30=nC50 then find nC78 ?

Answer 1

Answer:

Step-by-step explanation:

nC30=nC50

n = 30 + 50

  = 80

nC78 = 80C78

         = 80*79/2

          = 3160

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Answer 2

The value of ⁿC₇₈ is 3160

Given : ⁿC₃₀ = ⁿC₅₀

To find : The value of ⁿC₇₈

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of ⁿC₇₈)

Now, we know that :

$^{n} C_{r} = \: ^{n}C_{n - r}$

According to the above mentioned mathematical formula, we get :

ⁿC₃₀ = ⁿCₙ₋₃₀

And,

ⁿC₃₀ = ⁿC₅₀

Which implies,

ⁿCₙ₋₃₀ = ⁿC₅₀

Which also implies,

n-30 = 50

n = 50+30

n = 80

Now, the value of ⁿC₇₈ will be :

= ⁿC₇₈

= ⁸⁰C₇₈

$= \frac{80!}{(80 - 78)! \: \times \: 78! }$

$= \frac{80 \times 79 \times 78!}{2! \times 78!}$

$= \frac{80 \times 79}{2}$

$= 40 \times 79$

$= 3160$

(This will be considered as the final result.)

Used formula :

• $^{n}C_{r} = \frac{n!}{(n-r)!\times r!}$

Hence, the value of ⁿC₇₈ is 3160