Six boxes are numbered 1, 2, 3, 4, 5 and 6. Each box must contain either a white ball or a black ball. At least one box must contain a black ball and boxes containing black balls must be consecutively numbered. find the total number of ways of placing the balls.

In how many ways can 6 green toys and 6 red toys be arranged, such that 2 particular red toys are never together whereas 2 particular green toys are always together?

There are five comics numbered from 1 to 5. In how many ways can they be arranged, so that part-1 and part-3 are never together?

The number of ways which a mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same is:

Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

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