ID number

Akansha wrote:A company assigns ID number to employees. Each is to consist of 4
different digits from 0 to 9 inclusive except 1st digit cannot be 0. How many
different combinations are there?
a. 3024
b. 4536
c. 5040
d. 9000
e. 10000

OA is B

IMO B
Let the Four digit be denoted as ABCD
For first digit A i can choose any digit other than 0 = 9 digits
For B, i can choose any digit other than the one used for A = 9 digits(We can use 0 here)
For C, i can choose any digit other than the one used for A,B = 8 Digits
For D, i can choose any digit other than the one used for A,B,C = 7 Digits

So total combinations possible = 9*9*8*7 = 4536

Thanks

I concur with sameerballani.

4 digit combo with 10 possible digits. Math would normally be 10*9*8*7. However since the first digit can't be zero, the first digit has nine possibilities, and since the second digit may include zero, the second digit will have nine possibilities. So the math will be 9*9*8*7=4,536.

IMO B,

the ques is asking for different combinations, which you might missed while solving.

quick note on tedious multiplication in problems like this.

when you are down to 9 * 9 * 8 * 7 , try to calculate the unit digit of the product.

eg. 9*9 ---> unit digit is always 1, so deciding factor is the unit digit of the product 8*7 i.e 6

Only answer with unit digit as 6 is option B ..choose B and save precious 30 seconds for RC ;)

good point !!