Combinatorics: how many different 5-digit numbers, bigger than 20000, can be made...?

[rogik]

The question reads: how many different 5-digit numbers, bigger than 20000, can be made from the digits 1,2,3,4 if digits 2,3,4 are not repeated and digit 1 is repeated twice.

I used the formula for permutations with repetition because digit 1 is repeated twice and found:

5!/2! = 60. But the answer is wrong. My suspicion is that 60 is the total number of 5-digit numbers from these digits with digit 1 repeated twice... is that correct?

So, how do I get 5-digit numbers bigger than 20000?

Thanks.

 

[tkhunny]

#1 -- 2, 3, or 4 -- Call these x_i

There remain only a few patterns:

x_i, x_i, 1, 1
x_i, 1, x_i, 1
x_i, 1, 1, x_i
1, x_i, x_i, 1
1, x_i, 1, x_i
1, 1, x_i, x_i

Now what?

 

[Steven G]

#1 -- 2, 3, or 4 -- Call these x_i

There remain only a few patterns:

x_i, x_i, 1, 1
x_i, 1, x_i, 1
x_i, 1, 1, x_i
1, x_i, x_i, 1
1, x_i, 1, x_i
1, 1, x_i, x_i

Now what?

Multiply 4 by 6