# Arrangement of items after removing some of the items

1. Jul 9, 2014

### desmond iking

1. The problem statement, all variables and given/known data
A bag contains 4 red cubic blocks, 3 yellow cubic blocks, . Five cubic blocks are removed randomly from the bag and arranged in line . How many arrangements are possible?

the ans is 8 .

my working is 7P5/(4! X 3!) =17.5 .

my ans is rather weird.

2. Relevant equations

3. The attempt at a solution

2. Jul 9, 2014

### HallsofIvy

Staff Emeritus
Are we to assume that blocks of the same color are indistinguishable?

3. Jul 9, 2014

### Ray Vickson

The number of arrangements cannot possibly be 17.5; it cannot be fractional.

Instead of just writing down some formulas, you need to explain the logic, so that we are in a position to assist you. If your thinking is "off", we need to know first what it is before we can put you on the right track.

4. Jul 10, 2014

### desmond iking

my reasoning is first i choose 5 blocks from the 7 blocks. then since there 're 4 same colour red and 5 same colour yellow, so i divide it by 4! X 3!

5. Jul 10, 2014

### Fredrik

Staff Emeritus
You need to provide more information. Is that really the full problem statement? I don't see an interpretation that yields the answer 8. For example, if you end up choosing 4 red and 1 yellow, I'd say that 5 arrangements are possible, and if you end up choosing 3 red and 2 yellow, I'd say that 10 arrangements are possible.