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Texas Instruments technical mcq question, verified with a worked answer. Free to practise - no sign-up.
The Christmas carols
You are organizing a program for Christmas and want to form a choir group. You want the choir group to consist of 3 boys and 2 girls from a group of 7 boys and 10 girls.
In how many ways can you form the choir group if one boy and one girl refuse to sing together?
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Show answer & explanation
Total ways without restriction = C(7,3) * C(10,2) = 35 * 45 = 1575. Number of selections where both the specific boy and girl are chosen = C(6,2) * C(9,1) = 15 * 9 = 135. Total valid ways = 1575 - 135 = 1440.
Step-by-step Derivation:
Step 1: Total unrestricted ways to select 3 boys from 7 and 2 girls from 10: C(7,3) * C(10,2) = (35) * (45) = 1575.
Step 2: Cases where the incompatible boy B1 and girl G1 are both selected: choose remaining 2 boys from 6 and remaining 1 girl from 9: C(6,2) * C(9,1) = 15 * 9 = 135.
Step 3: Subtract incompatible selections: 1575 - 135 = 1440 ways.