# Quantitative Reasoning – Practice – 5-digit number questions!

PSA_PRACTICE_QNR17.

Ans:Let the five-digit number be EDCBA.

 E D C B A

Since the number is greater than 40000, the ‘E’ can be filled in by either 4 or 5. 2 ways.

Once, E is occupied (with either 4 or 5), D can be occupied by 4 remaining digits. 4 ways to fill D.

Similarly, C can be occupied by one among the rest 3 digits. 3 ways.

B & A can be occupied in 2 ways and 1 way respectively.

Total number of ways in which EDCBA can be formed= 2 * 4 * 3 * 2 *1= 48. There are 48 numbers that are greater than 40,000 which meet the conditions. Option B.

Another exercise would be to find out:

(i) the number of such 5 digit numbers using the digits 1,2,3,4,5 such that there is no restriction on number of times a digit is used. [Assuming all the 5 digit numbers to be greater than 40,000].

(ii) the number of such 5 digit numbers using the digits 1,2,3,4,5 such thatÂ they are all even-numbers.

[Assuming all the 5 digit numbers to be greater than 40,000].

(iii) the number of such 5 digit numbers using the digits 1,2,3,4,5 such thatÂ they are all even-numbers.[Assuming all the 5 digit numbers to be greater than 40,000].