can any one solve these GMAT Question

[aaratigarlapat]

In how many ways 5 different balls can be arranged in to 3 different boxes so that no box remains empty?

[MBAchase]

(1) 1 ball can be placed in 2 boxes each and 3 balls can be placed in the 3rd box. There are 3 ways in which we can do so.
This can be done in 3 * [5C1 * 4C1 * 3C3] = 3 * [5 * 4 * 1] = 3 * 20 = 60 ways

(2) 2 balls can be placed in 2 boxes each and 1 ball can be placed in the 3rd box. There are 3 ways in which we can do so.
This can be done in 3 * [5C2 * 3C2 * 1C1] = 3 * [10 * 3 * 1] = 90 ways

Total no. of ways = 60 + 90 = 150 ways

[aaratigarlapat]

(1) 1 ball can be placed in 2 boxes each and 3 balls can be placed in the 3rd box. There are 3 ways in which we can do so.
This can be done in 3 * [5C1 * 4C1 * 3C3] = 3 * [5 * 4 * 1] = 3 * 20 = 60 ways

(2) 2 balls can be placed in 2 boxes each and 1 ball can be placed in the 3rd box. There are 3 ways in which we can do so.
This can be done in 3 * [5C2 * 3C2 * 1C1] = 3 * [10 * 3 * 1] = 90 ways

Total no. of ways = 60 + 90 = 150 ways

thanks . but the Official Answer is 720 can you please help me to solve this problem.

[aaratigarlapat]

help me please to solve the problem......