Question

The value of n is: If nC3 = 10

Answer 1

Given:

nC3 = 10

To find:

The value of n

Solution:

The value of n is 5.

We can find the value by following the given steps-

We know that the value of n can be obtained by using the combination.

It is given to us that nC3 is equal to 10.

We know that using the combination, nCr=n!/r!(n-r)!

Here n is the total number of objects and r is the number of objects that are to be chosen.

Using the above formula, we get

nC3=n!/3!(n-3)!

=n(n-1)(n-2)(n-3)!/3!(n-3)!

=n(n-1)(n-2)/3×2×1

=n(n-1)(n-2)/6

Now, n(n-1)(n-2)/6=10

n(n-1)(n-2)=60

We will solve the LHS and then solve the equation,

n($n^{2}$-3n+2)=60

$n^{3}-3n^{2} +2n-60=0$

On factorizing, we get

(n-5)($n^{2} +2n+12)$=0

Now, (n-5)=0 and ($n^{2} +2n+12$)=0

On putting ($n^{2} +2n+12$)=0, we do not get a real solution.

So, n-5=0

n=5

Therefore, the value of n is 5.

Answer 2

The value of n = 5

Given :

$\displaystyle \sf{ {}^{n} C_3 = 10 }$

To find :

The value of n

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf{ {}^{n} C_3 = 10 }$

Step 2 of 2 :

Find the value of n

$\displaystyle \sf{ {}^{n} C_3 = 10 }$

$\displaystyle \sf{ \implies {}^{n} C_3 = 5 \times 2 }$

$\displaystyle \sf{ \implies {}^{n} C_3 = \frac{5 \times 4}{2} }$

$\displaystyle \sf{ \implies {}^{n} C_3 = \frac{5 \times 4 \times 3}{3 \times 2} }$

$\displaystyle \sf{ \implies {}^{n} C_3 = \frac{5 \times 4 \times 3 \times 2}{(3 \times 2) \times 2} }$

$\displaystyle \sf{ \implies {}^{n} C_3 = \frac{5 !}{3! \: 2!} }$

$\displaystyle \sf{ \implies {}^{n} C_3 = {}^{5} C_3 }$

$\displaystyle \sf{ \implies n = 5}$

Hence the required value of n = 5

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ IF 1/1!9!+1/3!7!+1/5!5!+1/7!3!+1/9!=2^n /10! then n=?

https://brainly.in/question/20427754

2. If (1+x+x2)n = a0 +a1x +a2x2 + a3x3+ ...+ a2nx2n,show thata0+a3+a6 + ... = 3n-1

https://brainly.in/question/8768959