Q9. If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, (i) the digits are repeated?
ANS: when repeatation are allowed, the 1st place can be filled in 2 ways by nos 5 and 7.If 1st place be 5 ,the 2nd place can be filled in 5 ways. 3rd place also can be filled in 5 ways.similarlly 4th place will be filled in 5 ways. But since the no. should be greater than 5000 =5*5*5 -1 =124 . If the 1st place be 7 then the total nos. which can be formed=5^3=125.
Hence total sample space =124+125=249
the no of favourable event i.e. nos. divisible by 5 =99
probablity=99/249
When the digits are repeated
Since four-digit numbers greater than 5000 are formed, the leftmost digit is either 7 or 5.
The remaining 3 places can be filled by any of the digits 0, 1, 3, 5, or 7 as repetition of digits is allowed.
∴Total number of 4-digit numbers greater than 5000 = 2 × 5 × 5 × 5 − 1
= 250 − 1 = 249
[In this case, 5000 can not be counted; so 1 is subtracted]
A number is divisible by 5 if the digit at its units place is either 0 or 5.
∴Total number of 4-digit numbers greater than 5000 that are divisible by 5 = 2 × 5 × 5 × 2 − 1 = 100 − 1 = 99
Thus, the probability of forming a number divisible by 5 when the digits are repeated is
.