Help Please .... Permutations And Combinations

What is the number of sequences with the length m+k which is constructed from k appearances of 0 and m appearances of 1?

here i think i know the answer :
(m+k)!/m!.k!

The second question is:
In how much sequences from the question above there is no adjacent appearances of 1. That is no appearances of 11?

find how many sets X that implies : |X| = 5 , X SUBSETS OR EQUALL to {1,2,3,...,14} and in X there exists no numbers that the difference between them is 1. In other words for every i, if i belongs to X, then i+1 doesn't belong to X

PLEASE GUYS CAN YOU HELP ME . I REALLY NEED IT

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Originally Posted by KOXKOXKOX

What is the number of sequences with the length m+k which is constructed from k appearances of 0 and m appearances of 1?
here i think i know the answer :
(m+k)!/m!.k!

[COLOR=black]The second question is:
In how much sequences from the question above there is no adjacent appearances of 1. That is no appearances of 11?

find how many sets X that implies : |X| = 5 , X SUBSETS OR EQUALL to {1,2,3,...,14} and in X there exists no numbers that the difference between them is 1. In other words for every i, if i belongs to X, then i+1 doesn't belong to X

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Your first answer is correct.

For the second we must have then the zeros form separators, like “_0_0_0_”, three zeros make four placesfor the 1's.
So the answer is .

The third answer is the same as: “How many strings of nine zeros and five ones are possible if no two ones are consecutive?”