Respuesta :

Given:

The combination C(14,10).

To find:

The value of the given combination.

Solution:

We know that,

[tex]C(n,r)=\dfrac{n!}{r!(n-r)!}[/tex]

Using this formula, we get

[tex]C(14,10)=\dfrac{14!}{10!(14-10)!}[/tex]

[tex]C(14,10)=\dfrac{14\times 13\times 12\times 11\times 10!}{10!(4)!}[/tex]

[tex]C(14,10)=\dfrac{14\times 13\times 12\times 11}{4\times 3\times 2\times 1}[/tex]

[tex]C(14,10)=7\times 13\times 11[/tex]

[tex]C(14,10)=1001[/tex]

Therefore, the value of C(14,10) is 1001 and the correct option is B.

The equivalent expression of "[tex]C(14,10)[/tex]" is "1001".

Equivalent expression:

using formula:

[tex]\to ^n C_r=\frac{n!}{r!(n-r)!}[/tex]

putting the given value into the above formula:

[tex]\to ^{14} C_{10}=\frac{14!}{10!(14-10)!}[/tex]

              [tex]=\frac{14 \times 13 \times 12 \times 11 \times 10! }{10! \times 4 \times 3 \times 2 \times 1}\\\\=\frac{14 \times 13 \times 12 \times 11 }{ 4 \times 3 \times 2 \times 1}\\\\={7 \times 13 \times 11 }{}\\\\=1001[/tex]

Therefore, the final answer is "1001".

Find out more information on the equivalent here:

brainly.com/question/17733453

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