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Standard XII

Mathematics

Combination

A committee o...

Question

A committee of $5$ members is to be formed from $6$ boys and $5$ girls. The number of ways in which the committee can be formed so that the committee must contain atleast one boy and one girl having majority of boys is

240

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245

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250

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275

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Solution

The correct option is D $275$
Required committee should contain $3$ boys , $2$ girls or $4$ boys , $1$ girl
$∴$ Number of ways for committee to be formed is
$=^{6} C_{3} \times^{5} C_{2} +^{6} C_{4} \times^{5} C_{1} = 275$

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Q. In a high school, a committee has to be formed from a group of

6

boys

M_{1}, M_{2}, M_{3}, M_{4}, M_{5}, M_{6},

and

5

girls

G_{1}, G_{2}, G_{3}, G_{4}, G_{5} .

(i) Let

α_{1}

be the total number of ways in which the committee can be formed such that the committee has

5

members, having exactly

3

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2

girls.
(ii) Let

α_{2}

be the total number of ways in which the committee can be formed such that the committee has atleast

2

members, and having an equal number of boys and girls.
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α_{3}

be the total number of ways in which the committee can be formed such that the committee has

5

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2

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(iv) Let

α_{4}

be the total number of ways in which the committee can be formed such that the committee has

4

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\begin{matrix} L I S T - I & L I S T - I I P . & The value of α_{1} is & 1. & 136 Q . & The value of α_{2} is & 2. & 189 R . & The value of α_{3} is & 3. & 192 P . & The value of α_{4} is & 4. & 200 5. & 381 6. & 461 \end{matrix}

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Combination

Standard XII Mathematics

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A committee of 5 members is to be formed from 6 boys and 5 girls. The number of ways in which the committee can be formed so that the committee must contain atleast one boy and one girl having majority of boys is

The correct option is D 275Required committee should contain 3 boys ,2 girls or 4 boys ,1 girl ∴Number of ways for committee to be formed is =6C3×5C2+6C4×5C1=275

A committee of $5$ members is to be formed from $6$ boys and $5$ girls. The number of ways in which the committee can be formed so that the committee must contain atleast one boy and one girl having majority of boys is

The correct option is D $275$
Required committee should contain $3$ boys , $2$ girls or $4$ boys , $1$ girl
$∴$ Number of ways for committee to be formed is
$=^{6} C_{3} \times^{5} C_{2} +^{6} C_{4} \times^{5} C_{1} = 275$