Question

The value of 10C3 + 8C2 is
1.248
2. 145
3. 108
4. 148​

Answer 1

Answer:

the value is 148. I think this is the answer.

Answer 2

$\displaystyle \sf{ {}^{10}C_3 +{}^{8}C_ 2} = 148$

Given :

The expression

$\displaystyle \sf{ {}^{10}C_3 +{}^{8}C_ 2}$

To find :

The value of the expression

1. 248

2. 145

3. 108

4. 148

Formula :

$\displaystyle \sf{ {}^{n} C_r = \frac{n!}{r!(n - r)!} }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ {}^{10}C_3 +{}^{8}C_ 2}$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ {}^{10}C_3 +{}^{8}C_ 2}$

$\displaystyle \sf{ = \frac{10!}{3!(10 - 3)!} + \frac{8!}{2!(8 - 2)!} }$

$\displaystyle \sf{ = \frac{10!}{3! \: 7!} + \frac{8!}{2! \: 6!} }$

$\displaystyle \sf{ = \frac{10 \times 9 \times 8 \times 7!}{3! \: 7!} + \frac{8 \times 7 \times 6!}{2! \: 6!} }$

$\displaystyle \sf{ = \frac{10 \times 9 \times 8}{3! } + \frac{8 \times 7 }{2! } }$

$\displaystyle \sf{ = \frac{10 \times 9 \times 8}{3 \times 2 \times 1 } + \frac{8 \times 7 }{2 \times 1 } }$

$\displaystyle \sf{ =120 + 28 }$

$\displaystyle \sf{ =148 }$

Hence the correct option is 4. 148