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Q).the number of ways of choosing 2boys and 2 girls in a class for a game of mixed doubles is 1620 .then the number of ways of
choosing 2 students in the class is
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india12317:
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Answer:
171
Step-by-step explanation:
Let the number of boys and number of girls be a and b respectively.
ᵃC₂ * ᵇC₂ = 1620
a ! / 2! (a-2)! * b ! / 2! (b-2)! = 1620
a(a-1) * b(b-1) = 1620 * 2 * 2
a(a-1) * b(b-1) = 2² *2² * 3⁴ * 5
a(a-1) * b(b-1) = 10 * 9 * 9 * 8
Thus by the observation
a = 10 and b =9
thus the total number of students in the class = a+b = 10+9 = 19
therefore the number of ways of choosing 2 students out of 19 is
¹⁹C₂ = 19! / 2! * 17! = 19 *18 / 2 = 171
Hope this helps you.
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