Q1. A number of 4 different digits is formed by using 1, 2, 3, 4, 5, 6, 7. Find

the probability that it is divisible by 5.

Q2.A bag contains 5 red, 4 blue and an unknown number of m green balls.Two balls are drawn. If probability of both being green is 1/7 find m.

(1)

The total four digit numbers that can be formed by the digits 1, 2, 3, 4, 5, 6, 7 are 7 × 6 × 5 × 4 = 840

Total four digit numbers that can be formed by the digits which is divisible by 5 are:

For the number to be divisible by 5, the last digit must be 5.

So, the number of such numbers are 6 × 5 × 4 = 120. (it is given in the question that the number should be formed by different digits)

The probability that it is divisible by 5 =

(2)

The number of red balls = 5, the number of blue balls = 4, the number of green balls = *m*

Total number of balls = 5 + 4 + *m* = 9 + *m*

Since two balls are drawn, the number of ways in which both the balls being drawn are green =

Total number of ways in which two balls can be drawn are

Probability =

since the number of balls can never be negative,

So, *m* = – 2 is rejected.

Hence, *m* = 6

Thus, the number of green balls = 6.

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