In how many ways can `6` children be arranged taking `4` at a time, so that the youngest child is always taken?

In how many ways can 5 children be arranged in a line such that two particular children of them are always together

In how many ways can 5 children be arranged in a line such that : two of them, Ram and Shyam are always together?

In how many ways can 5 children the arranged in a row such that two of them, Ram and Shyam, are always together? two of them, Ram and Shyam, are never together?

Eight children are to seated on a bench. (i) In how many ways can the children be seated ? (ii) How many arrangements are possible if the youngest child slits at the left hand end of the bench ?

In how many ways can 9 things be arranged taken 4 at time , and in how many of these arangements will a particular thing be included?

In how many ways can 5 children the arranged in a row such that two of them,Ram and Shyam,are always together? two of them, Ram and Shyam,are never together?

In how many ways the 26 English letters can be arranged along a line so that all the 5 vowels must occur always after the letter 'B'.

In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together?

In how many ways 10 different books can be arranged in an almirah such that a particular book (1) is always taken (2) is never taken