A group of volleyball players consists of four grade 11 students and six grade 12 students. If six players are chosen at random to start a match, what is the probability that three will be from each grade?

Answer 1

Probability that three will be from each grade #=0.36#

Given -

Four grade students#= 11#
Six grade students #=12#

Probability that three will be from each grade #=0.36#

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Answer 2

To find the probability that three players will be from each grade when six players are chosen at random:

  1. Calculate the total number of ways to choose six players from the group of ten players.
  2. Calculate the number of ways to choose three grade 11 students out of four and three grade 12 students out of six.
  3. Multiply the number of ways to choose three players from each grade by the number of combinations in step 2.
  4. Divide the result from step 3 by the total number of combinations in step 1 to find the probability.

Let's calculate it:

Total number of ways to choose six players from ten: ( \binom{10}{6} = 210 )

Number of ways to choose three grade 11 students from four: ( \binom{4}{3} = 4 )

Number of ways to choose three grade 12 students from six: ( \binom{6}{3} = 20 )

Total number of ways to choose three players from each grade: ( 4 \times 20 = 80 )

Probability = ( \frac{80}{210} )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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