Q. 215.0( 1 Vote )

How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 8000, if repetition of digits is not allowed?

Answer :

Given: Four-digit number is required which is greater than 8000


Assume four boxes, now in the first box can either be one of the two numbers 8 or 9, so there are two possibilities which is 2C1


In the second box, the numbers can be any of the four digits left, so the possibility is 4C1


Similarly, for the third box, the numbers can be any of the three digits left, so the possibility is 3C1


for the fourth box, the numbers can be any of the two digits left, so the possibility is 2C1


Hence total number of possible outcomes is 2C1 × 4C1 × 3C1 × 2C1 = 2 × 4 × 3 × 2 = 48


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