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luda_lava [24]
3 years ago
14

The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How man

y different teams made up of two girls and two boys could be chosen?
Mathematics
1 answer:
cestrela7 [59]3 years ago
5 0

Answer:

Total\ Selection = 30\ ways

Step-by-step explanation:

Given

Girls = 3

Boys = 5

Required

How many ways can 2 boys and girls be chosen?

The keyword in the question is chosen;

This implies combination and will be calculated as thus;

Selection =\  ^nC_r = \frac{n!}{(n-r)!r!}

For Boys;

n = 5 and r = 2

Selection =\  ^5C_2

Selection = \frac{5!}{(5-2)!2!}

Selection = \frac{5!}{3!2!}

Selection = \frac{5 * 4 * 3!}{3!*2 * 1}

Selection = \frac{20}{2}

Selection = 10

For Girls;

n = 3 and r = 2

Selection =\  ^3C_2

Selection = \frac{3!}{(3-2)!2!}

Selection = \frac{3!}{1!2!}

Selection = \frac{3 * 2!}{1 *2!}

Selection = \frac{3}{1}

Selection = 3

Total Selection is calculated as thus;

Total\ Selection = Boys\ Selection * Girls\ Selection

Total\ Selection = 10 * 3

Total\ Selection = 30\ ways

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Given :-

  • a² - 2a - b² = 0
  • 2b + 2ab = 0

To find :-

  • Value of a and b .

Solution :-

<u>Taking</u><u> </u><u>second</u><u> </u><u>equation</u><u>:</u><u>-</u>

  • 2b + 2ab = 0
  • 2b ( 1 + a ) = 0
  • 2b = 0 or (1+a) = 0
  • b = 0 , a = -1

<u>Substitute</u><u> </u><u>in </u><u>first </u><u>equation</u><u> </u><u>:</u><u>-</u><u> </u>

  • a² - 2a - b² = 0

<u>When </u><u>b </u><u>=</u><u> </u><u>0</u><u> </u><u>,</u>

  • a² - 2a - 0² = 0
  • a² - a = 0
  • a( a -1) =0
  • a = 0 , 1

<u>When </u><u>a </u><u>=</u><u> </u><u>-</u><u>1</u><u> </u><u>,</u>

  • (-1)² - 2*(-1) - b² = 0
  • 1 + 2 - b² = 0
  • b² = 3
  • b = ±√3

<u>Answer </u><u>:</u><u>-</u><u> </u>

  • a = 0,1 ; b = 0
  • a = -1 , b = ±√3
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