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There are $3$ applicants for a scholarship in Physics,$5$ for Mathematics,and $4$ for Chemistry. In how many different ways can these scholarships be awarded such that at least one scholarship is awarded in each subject?

How many words can be formed using any $3$ letters from the word $UNIVERSAL$?

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$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is:

The number of different permutations that can be formed by taking $4$ letters at a time from the letters of the word '$REPETITION$' is

The number of ways in which all the letters of the word $COMBINATION$ can be arranged so that the vowels always come together is:

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