Question

What is the value of 8co-8c1+8c2-8c3+8c4-8c5+8c6-8c7+8c8?

Answer 1

Answer:

44

Step-by-step explanation:

8-8+1=1

1+8+2=11

11-8+3=6

6+8+4=18

18-8+5=15

15+8+6=29

29-8+7=28

28+8+8=44ans

Answer 2

$^8C_0+^8C_1+^8C_2+^8C_3+^8C_4+^8C_5+^8C_6+^8C_7+^8C_8=256$

Step-by-step explanation:

Given : Expression $^8C_0+^8C_1+^8C_2+^8C_3+^8C_4+^8C_5+^8C_6+^8C_7+^8C_8$

To find : What is the value of expression ?

Solution :

We know, the formula of combination is $^nC_r=\frac{n!}{r!(n-r)!}$

Applying in the expression,

$^8C_0+^8C_1+^8C_2+^8C_3+^8C_4+^8C_5+^8C_6+^8C_7+^8C_8$

$=\frac{8!}{0!(8-0)!}+\frac{8!}{1!(8-1)!}+\frac{8!}{2!(8-2)!}+\frac{8!}{3!(8-3)!}+\frac{8!}{4!(8-4)!}+\frac{8!}{5!(8-5)!}+\frac{8!}{6!(8-6)!}+\frac{8!}{7!(8-7)!}+\frac{8!}{8!(8-8)!}$

$=\frac{8!}{0!8!}+\frac{8\times 7!}{1!7!}+\frac{8\times 7\times 6!}{2\times 6!}+\frac{8\times 7\times 6\times 5!}{3\times 2\times 5!}+\frac{8\times 7\times 6\times 5\times 4!}{4\times 3\times 2\times 4!}+\frac{8\times 7\times 6\times 5!}{5!\times 3\times 2}+\frac{8\times 7\times 6!}{6!2\times 1}+\frac{8\times 7!}{7!\times 1}+\frac{8!}{8!0!}$

$=1+8+28+56+70+56+28+8+1$

$=256$

Therefore, $^8C_0+^8C_1+^8C_2+^8C_3+^8C_4+^8C_5+^8C_6+^8C_7+^8C_8=256$

#Learn more

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