How many combinations are there for a 5 digit code using 3 2s and 2 4s?

Answer 1

There are five digits all together. The number of ways of arranging them is

5 x 4 x 3 x 2 x 1 = 120 .

But the three 2s can be arranged in 3 x 2 = 6 different ways and they all look the same.

And the two 4s can be arranged in 2 different ways and they look the same.

So out of the 120 different ways of arranging all five, there's a group of six

for every possible arrangement of the 2s that all look the same, and there's

a group of two for each possible arrangement of the 4s that both look the

same.

The number of combinations that look different is 120/(6 x 2) = 10 .

And here they are:

2 2 2 4 4

2 2 4 2 4

2 2 4 4 2

2 4 2 2 4

2 4 2 4 2

2 4 4 2 2

4 2 2 2 4

4 2 2 4 2

4 2 4 2 2

4 4 2 2 2