A bag contains 10 different balls. Five balls are drawn simultaneously and then replaced and then seven balls are drawn. The probability that exactly three balls are common to the two drawn is , then the value of  is

(5)

The number of ways of drawing 7 balls (second draws)

For each set of 7 balls of the second draw, 3 must be common to the set of 5 balls of the first draw, i.e., 2 other balls can be drawn in  ways

Thus, for each set of 7 balls of the second draw, there are  ways of making the first draw so that there are 3 balls common

Hence, the probability of having three balls in common is