Question

The students in a class are selected at random, one after the other for an examination. Find the probability p that the boys and girls in the class are alternate if (i) the class consists of four boys and three girls,​

Answer 1

n(s)=7

n(s)=7n(e)=4

P (Getting a boy)=4/7

P(Getting a Girl)=3/7

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Answer 2

The probability p that the boys and girls in the class are alternate is 1/35.

• The class consists of 4 boys and 3 girls.

Total number of students in the class is 7

• Number of ways in which the students can be arranged is 7! = 5040.

• Now we have to arrange the boys and girls so that boys and girls sit alternate to each other.

Now to arrange boys in the seating arrangement is to start with a boy and end with a boy .

• 4 places are to be occupied in 4 ways, therefore there are 4! ways to arrange the boys in the arrangement.

• Similarly to arrange 3 girls between the boys there is 3! ways.

• Total number of ways to arrange in the alternate arrangement is 3! × 4! = 24 × 6 = 144 ways.

• Now probability is 144/5040 = 1/35. A