Permutation And Combination Mock Tests

The number of 3-digit numbers from digits 1,2,3,4,5 without repetition is:

The value of 5! is:

Six points A, B, C, D, E, and F are marked on a straight line in that order. Points P, Q, R, S, and T are marked on another straight line in that order. How many triangles can be formed by choosing any three points from these eleven points, provided the three points are not collinear?

In how many ways can 5 different books be distributed among 3 children so that each child gets at least one book?

In how many ways can the letters of the word "EDUCATION" be arranged so that all vowels come together?

In how many different ways can the letters of the word "LOGIC" be arranged so that the vowels always come together?

In how many different ways can the letters of the word "PERMUTATIONS" be arranged?

In how many different ways can the letters of the word 'EDUCATION' be arranged such that all vowels come together?