From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition, including at least 4 boys and 4 girls. The 2 girls who won the prize last year should be included. In how many ways can the selection be made?
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Two particular girls are always chosen. So it remains that
From 12 boys 8 girls, :: 8 students to be chosen.
with at least 4 boys and 2 girls.
total 4 boys, 6 girls, or 5 boys 5 girls or 6 boys and 4 girls... possible.
number of ways: 12C4 * 8C4 + 12C5 * 8C3 + 12C6 * 8C2
= 12*11*10*9*8*7*6*5/(24 *24) + 12*11*10*9*8*8*7*6/(120*6)
+ 12*11*10*9*8*7*8*7/(720*2)
= 12*11*10*9*7 [5/12 + 8/15 + 14/45 ] = 462 * [75+96+56]
= 462 * 227
From 12 boys 8 girls, :: 8 students to be chosen.
with at least 4 boys and 2 girls.
total 4 boys, 6 girls, or 5 boys 5 girls or 6 boys and 4 girls... possible.
number of ways: 12C4 * 8C4 + 12C5 * 8C3 + 12C6 * 8C2
= 12*11*10*9*8*7*6*5/(24 *24) + 12*11*10*9*8*8*7*6/(120*6)
+ 12*11*10*9*8*7*8*7/(720*2)
= 12*11*10*9*7 [5/12 + 8/15 + 14/45 ] = 462 * [75+96+56]
= 462 * 227
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