How to assign the rooms?

the 5 girs have to be arranged in 2,2,1 manner. .so in this manner there can be (5C2×3C2)/2!=15 groups which is also total no of ways that the boy and the girls can be arranged into 4 groups. now simply the answer is 15×4!=360

Write down the 6 names in any of the 6! = 720 possible ways, and look at where Frank's name falls.

If he is first on the list, F _ _ _ _ _ , there are 120 of these for the 5! orders of the girls' names. We can choose any of the 3 other rooms to be the single, then the room assignments to rooms 1, 2, 3, and 4 are (F, single, double, double) or (F, double, single, double), or (F, double, double, single). but then it doesn't matter which order the names for the doubles occur, so for this case we have 120 * 3 / 4 = 90 ways.

And the same if Frank is #6 on the list at the other end, for a total of 180.

If he is 2nd, we have _ F _ _ _ _, and now room 1 must be the girls' single, room 2 is Frank's, and the others are doubles. But again, we are counting those twice for switching the occupants of the doubles, so we have 120 / 4 = 30 ways for this, and another 30 for where Frank is #5 on the list.

If Frank is #3 on the list, we have _ _ F _ _ _ and now the rooms can be (double, Frank, single, double), or (double, Frank, double, single). But again, that counts each arrangement 4 times, so we have 120 * 2 / 4 = 60. And another 60 when Frank is #4 on the list.

Adding that all up: 180 + 60 + 120 = 360 ways, same as above.