Respuesta :
Answer:
[tex]^{15} C_{5} = 3,003 \\[/tex]
Step-by-step explanation:
here , we want to evaluate the value of 15 combination 5
Mathematically, we have the general combination formula as follows;
[tex]{n} C^{r} =\frac{n!}{(n-r)!r!}[/tex]
In this case , n is 15 and r is 5
Thus , we have it that;
[tex]^{15} C_{5} = \frac{15!}{(15-5)!5!} \\= \frac{15!}{10!5!} =\frac{15x14x13x12x11x10!}{10!5!} \\=\frac{15x14x13x12x11}{5!} \\\frac{15x14x13x12x11}{5x4x3x2xx1}=3,003\\[/tex]
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After evaluating, we get [tex]^{15} C_{5}=3003[/tex]
Combination :
The combination of selecting r object from n object is given as,
[tex]^{n} C_{r}=\frac{n!}{r!(n-r)!}[/tex]
We have to find [tex]^{15} C_{5}[/tex].
[tex]^{15} C_{5}=\frac{15!}{5!*10!} \\\\^{15} C_{5}=\frac{15*14*13*12*11*10!}{(5*4*3*2*1)*(10!)} \\\\^{15} C_{5}==\frac{360360}{120} \\\\^{15} C_{5}=3003[/tex]
Learn more about the Permutation and combination here:
https://brainly.com/question/11732255
