Question

Question 8
There are 7 boys and 8 girls and need to form a team of 5 boys and 6 girls. In how many ways can the team be formed?
432
481
ОО
588
232

Answer 1

SOLUTION

GIVEN

There are 7 boys and 8 girls and need to form a team of 5 boys and 6 girls

TO CHOOSE THE CORRECT OPTION

The number of ways the team can be formed

• 432

• 481

• 588

• 232

EVALUATION

Here it is given that

Total number of boys = 7

Total number of girls = 8

Now we have to form a team of 5 boys and 6 girls

So the number of ways in which 5 boys can be selected from 7 boys

$\sf{ = {}^{7}C_{5} \: }$

$\displaystyle \sf{ = \frac{7! }{5! \: 2! } \: }$

$\displaystyle \sf{ = \frac{7 \times 6 }{2} \: }$

$\displaystyle \sf{ = 21}$

Again the number of ways in which 6 girls can be selected from 8 girls

$\sf{ = {}^{8}C_{6} \: }$

$\displaystyle \sf{ = \frac{8! }{6! \: 2! } \: }$

$\displaystyle \sf{ = \frac{8 \times 7}{2} \: }$

$\displaystyle \sf{ = 28}$

Hence the number of ways the team can be formed

$\sf{ = 21 \times 28\: }$

$\sf{ = 588\: }$

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Answer 2

Answer:

Ste56p-by-step explanation: