CAT 2016 expected question:

How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?

A] 499

B] 500

C] 375

D] 376

E] 501

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Solution:

The smallest number in the series is 1000, a 4-digit number.

The largest number in the series is 4000, the only 4-digit number to start with 4.

The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.

The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.

Including 4000, there will be 376 such numbers.

Method 2

numbers starting with 1= 5*5*5 ( fixing 1 on thousand digit and then we have 5 choices for filling three places of 4 digit no. )

numbers starting with 2= 5*5*5 ( fixing 2)

numbers starting with 3=5*5*5 (fixing 3)

finally the no. 4000

total nos. = (125*3)+1 =376