How many numbers greater than 56000 can be formed by using the digits 4, 5, 6, 7, 8 ; no digit being repeated in any number?
Answers
Answer:
90
Step-by-step explanation:
Given
How many numbers greater than 56000 can be formed by using the digits 4, 5, 6, 7, 8 ; no digit being repeated in any number?
Now total number of digits is 5. After 5 we can get 6,7 and 8. So we have 3 ways. Again we can take 4,7 and 8. So we get 3 ways. So 3 x 3! = 3 x 3 x 2 x 1 = 18. If first digit is 6 then remaining will be 4!
So total number of 5 digit number = 18 + 3 x 4!
= 18 + 3 x 24
= 18 + 72
= 90
OR
Total number of arrangements is 5!
Total number of arrangements having 4 in first place = 4!
Total number of arrangements having 5 in first place and 4 in second place will be 3!
So numbers greater than 56000 will be 5! – 4! – 3!
= 5 x 4 x 3 x 2 x 1 – 4 x 3 x 2 x 1 – 3 x 2 x 1
= 120 – 24 – 6
= 120 – 30
= 90