prob

Now for 5 similar apples:

For 5 apples in 2 similar boxes: (5,0); (4,1);(3,2).
For 4 apples in 2 similar boxes: (4,0); (3,1);(2,2).


3 ways - 5 0
3 ways -4 1
2 ways -3 2
2 ways-2 3
1 way -1 4
1 way - 0 5

So 12 ways. - -- For Apples


Now for 4 diff oranges:

For 4 oranges in 2 sim boxes: (4,0) – 1 way;
(3,1) – 4c3 or 4 ways;
(2,2) – 4c2 or 6 ways;
So total – 11 ways.

For 3 oranges in 2 sim boxes: (3,0) – 1 way
(2,1) – 3c2 or 3 ways.
So total – 4 ways * 4c3 for selecting 3 = 16 ways


For 2 oranges in 2 sim boxes: (2,0)- 1 way
(1,1)- 2 ways
So total – 3 ways * 4c2 for selecting 2 = 18 ways.
For 1 orange, 1 way only either of boxes – so 1 * 4c1 = 4 ways.
So,

For Oranges –

4 0 – 11 ways
0 4 – 1 way
3 1 – 16 ways
1 3 – 4 ways
2 2 - 18 ways

So total - 50 ways --- Apples.

So Total – 50 * 12 = 600 ways.