Multiple choice

Directions : Select the correct alternative from the given choices. A, B, C, D, E, F, G and H are 8 students in a school. The class teacher wants to send 4 students each for a quiz competition and drawing competition such that each student goes for exactly one competition. Assuming that each student is capable of participating in either of the two competitions, in how many ways can the class teacher create the two teams?

  1. 70

  2. 72

  3. 75

  4. 80
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We need to choose 4 students out of 8 for the first competition; the remaining 4 automatically go to the second. The number of ways is 8C4 = (8*7*6*5) / (4*3*2*1) = 70.

AI explanation

The teacher must divide the 8 distinct students into two teams of 4, with one team going to the quiz competition and the other to the drawing competition. The number of ways to choose 4 students out of 8 for the quiz competition is calculated using the combination formula 8C4. This gives (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70. Because the remaining 4 students automatically form the drawing team, the total number of ways is 70.

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