Question

If 22cr is the largest binomial coefficient in the expansion of (1+x)^22 find the value of 13 cr

Answer 1

Answer:

78

Step-by-step explanation:

22cr largest when r=n/2 so n is 22 then r is 11 then 13cr is 13c11 which is 78

Answer 2

Answer:

the value of $^{13}C_r=78$

Step-by-step explanation:

$(1+x)^{22}$

Facts: The largest cofficient in the expansion of $(1+x)^{n}$ is $^{22}C_\frac{n}{2}$ if n is even

Here,

$n=22$, So greatest cofficient in the expansion of $(1+x)^{22}$ is $^{22}C_\frac{22}{2}=^{22}C_{11}$

So,

$r=11$

$^{13}C_r=^{13}C_{11}=78$

$^{13}C_r=78$

About binomial coefficient:
The binomial coefficient in combinatorics is used to represent the variety of ways that a given subset of objects of a specific numerosity can be selected from a bigger collection.

It may be used to express the coefficients of the expansion of a power of a binomial, which is how it got its name.

It is defined as follows:

$\frac{n}{k} =\frac{n!}{(n-k)!k!}$

where a factorial is indicated by the exclamation point.

The factorial of a natural number is defined as the product of $n$ natural numbers less than or equal to $n$:

$n!=n.(n-1).....2.1$ and that, by convention, $0!=1$.

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