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? (ii) the repetition of digits is not allowed?

Answer

N/a

Explanation

(i) When repetition of digits is allowed, 5000 or greater number `=2xx5xx5xx5=250`
`:.` One number is 5000 in it.
`:.` Total numbers greater than `5000=250-1=249`
5000 or greater number divisible by 5
`=2xx5xx5xx2=100`
`:.` Numbers divisible by 5 and greater than 5000
`=100-1=99`
Now, required probability `=99/249=33/83`
(ii) Given digits `=0,1,3,5,7`
For the number of 4 digits greater than 5000, there will be 5 or 7 at thousand's place.
`:.` No. of ways to fill thousands's place `=2`
No. of ways to fill remaining 3 place from 3 digits out of remaining 4 digits.
`=.^(4)P_(3)=24`
`:.` Total numbers `=2xx24=48`
In the numbers divisible by 5
0 or 5 occur at unit place.
Taking at 0 unit place,
No. of ways of fill thousand's place `=2`
(taking 5 or 7) brgt No of ways to fill remaining two places `=.^(3)P_(2)=6`
Total ways `=2xx6=12`
Taking 5 at unit place,
No. of ways to fill thousand's place `=1`
(taking 7 only)
No. of ways to fill remaining two plaes `=.^(3)P_(2)=6`
Total ways `=1xx6=6`
Now numbers divisible by `5=12+6=18`
`:.` Required probability `=18/48=3/8`