Permutations and Combinations Level - 3

The number of ways in which four particular persons $A, B, C, D$ and six more persons can stand in a queue so that $A$ always stands before $B$, $B$ always before $C$ and $C$ always before $D$ is

The number of circles that can be drawn out of 10 points of which 7 are collinear is

How many different 9-digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?

How many diagonals are there in an $n$-sided polygon ($n > 3$)?

A polygon has 54 diagonals. Find the number of sides.

The number of natural numbers of two or more than two digits in which digits from left to right are in increasing order is

In how many ways can a cricketer score 200 runs with fours and sixes only?

A dice is rolled six times. One, two, three, four, five and six appears on consecutive throws of dice. How many ways are possible of having 1 before 6?

The number of permutations of the letters $a, b, c, d, e, f, g$ such that neither the pattern 'beg' nor 'acd' occurs is

In how many ways can the letters of the English alphabet be arranged so that there are seven letters between the letters $A$ and $B$?