How many different four - figure numbers can be made using the digits 1, 9, 9, 1?

Question

How many different four - figure numbers can be made using the digits 1, 9, 9, 1?

 

a. 6

b. 12

c. 16

d. 24

 

Answer 1

1199

1991

1919

9911

9119

9191

6 numbers

if all the digits were different you would have 4*3*2*1=24

you pick from 4 for the first digit, from 3 for the second digit, from 2 for the third digit and from 1 for the fourth digit

because you have 2 1s you divide 24 by 2 to get 12 and because you also have 2 9s you divide 12 by 2 to get 6

Answer 2

Lets try different combinations, start from the first number to the last number.

 

1111

9999

 

1911

1119

 

1991

9119

 

1919

9191

 

So far I have listed 8 combinations.  There could be more.  So your answer must be (b).

 

Another way to find out is to use the nCr function on you calculator.  Since you have 4 numbers in total and only 2 numbers repeat, your function will be

 

4 nCr 2

 

This will give you 12.

 

 

 

 

 

 

 

Answer 3

By simply writing out the possibilities we find that there are 6 possibilities.

 

1919

1991

9119

9191

1199

9911