1 year ago

In how many ways can 3person study groups beselected from a class of 25students?Note: nrn!r!(n-r)!nEnter

Mathematics

1 answer:

nlexa [21]1 year ago

8 0

Answer:

2,300

Explanation:

This is given as:

$\begin{gathered} 25\text{ combination 3 represented as:} \\ ^nC_r=\frac{n!}{r!(n-r)!} \\ n=25 \\ r=3 \\ ^{25}C_3=\frac{25!}{3!(25-3)!} \\ ^{25}C_3=\frac{25\times24\times23\times22!}{3!\times22!} \\ ^{25}C_3=\frac{25\times24\times23}{3\times2\times1} \\ ^{25}C_3=2300 \end{gathered}$

Therefore, there are 2,300 ways that 3 persons can be selected from 25 people

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For any integer x,x2-x will always produce an even value

Levart [38]

Consider expression $x^2-x.$ First, you can factor it:

$x^2-x=x(x-1).$

Since x is integer number, then you can see that x-1 is previous integer number (x-1 is 1 unit smaller than x).

Therefore, x-1 and x are two consecutive integers. When you have two consecutive integers, one of them is always even and one is always odd. Multiplying even integer number by odd integer number you always get even integer number.

Thus, $x^2-x$ is always even.