A person has $12$ friends out of which $7$ are relatives. In how many ways can he invite $6$ friends if at least $4$ of them should be his relatives

487

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462

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488

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502

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Solution

The correct option is B $462$
$12$ friends $⟶ 7$ are relatives
$5$ friends only $⟶$ Atleast $4$ relatives of $6$
$\Rightarrow^{5} C_{2}^{7} C_{4} +^{5} C_{1}^{7} C_{5} +^{5} C_{0}^{7} C_{6} \Rightarrow 10 (35) + 5 (21) + 7 \Rightarrow 462$
Therefore number of ways of inviting $= 462$
Option $: B$

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A person has 12 friends out of which 7 are relatives. In how many ways can he invite 6 friends if at least 4 of them should be his relatives

The correct option is B 46212 friends ⟶7 are relatives 5 friends only ⟶ Atleast 4 relatives of 6⇒5C72C4+5C71C5+5C70C6⇒10(35)+5(21)+7⇒462Therefore number of ways of inviting =462Option :B

A person has $12$ friends out of which $7$ are relatives. In how many ways can he invite $6$ friends if at least $4$ of them should be his relatives