Question

10C1 + 10C3 + 10C5 + 10C7 + 10C9 is equal to

Answer 1

Answer:512

Step-by-step explanation:

10C1=10

10C3= 120

10C5=252

10C7=120

10C9=10

Therefore by adding we get;

10+120+252+120+10=512

Answer 2

$^{10}C_1+^{10}C_3+^{10}C_5+^{10}C_7+^{10}C_9=512$

Step-by-step explanation:

Given : Expression $^{10}C_1+^{10}C_3+^{10}C_5+^{10}C_7+^{10}C_9$

To find : The value of the expression ?

Solution :

The formula of combination is $^nC_r=\frac{n!}{r!(n-r)!}$

 $^{10}C_1+^{10}C_3+^{10}C_5+^{10}C_7+^{10}C_9$

Applying in the expression,  

$=\frac{10!}{1!(10-1)!}+\frac{10!}{3!(10-3)!}+\frac{10!}{5!(10-5)!}+\frac{10!}{7!(10-7)!}+\frac{10!}{9!(10-9)!}$

$=\frac{10\times 9!}{1\times 9!}+\frac{10\times 9\times 8\times 7!}{3\times 2\times7!}+\frac{10\times 9\times 8\times 7\times 6\times 5!}{5\times 4\times 3\times 2\times 5!}+\frac{10\times 9\times 8\times 7!}{3\times 2\times7!}+\frac{10\times 9!}{9!\times 1!}$

$=10+120+252+120+10$

$=512$

Therefore, $^{10}C_1+^{10}C_3+^{10}C_5+^{10}C_7+^{10}C_9=512$

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