A grandmother is cleaning out her garage and finds 6 items that she no longer wa

Question

A grandmother is cleaning out her garage and finds 6 items that she no longer wants to store. She has two charities that she likes to donate to, so she is going to put the 6 items into two boxes. She wants to give at least one item to each charity. She does not care which charity gets which items, so the boxes are not labeled. How many different ways are there for her to place the 6 items into 2 unlabeled boxes? is another For example 1,2,3,4),15,6)3 is one way and 1,2,4,5),13,6 But 1,2,3,4,6),(51 is the same as 15) 1,2,34,6). 31 O 15 O 12 30 O 11 O 36

Explanation / Answer

She has to put 6 items in two unlabeled boxes and she wants to give at least one item to each charity.

so she put item 1 in any box (as boxes are unlabeled so doesn't matter which box)

After putting item 1 she has two options for putting item 2 in a box (one which is empty and one which contains item 1)

Also for item 3 she has two choices. same for 4, 5 and 6 item.

so she has 25 =32 ways.

But there is a case if all items came in one box, so we have to subract this one case

so required number of ways =32-1 = 31

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