Question

A delegation of four students is to be selected from a total of $12$ students.In how many ways can the delegation be selected If two particular students do not wish to be together in the delegation.

• A. $500$
• B. $870$
• C. $250$
• D. $175$

Answer 1

The correct option is B $870$

$4$ Student of $12$ students

Case 1 : $2$ are always exclded

$\Rightarrow 4$ Student of $10$ Students

Number of ways

${=}^{10}{C}_4=210$

Case 2 : Either of One is included

$=2{\times }^{11}{C}_4=2\times \frac{11\times 10\times 9\times 8}{4\times 3\times 2\times 1}=660$

Therefore Total ways

$=660+210$

$=870$ Ways