M L Aggarwal Solutions for Chapter: Permutations and Combinations, Exercise 2: EXERCISE 8.2

Eight children are to be seated on a bench. In how many ways can the children be seated?

Eight children are to be seated on a bench. How many arrangements are possible if the youngest child sits at the left hand end of the bench?

A number lock on a suitcase has $3$ wheels each labeled with ten digits from $0$ to $9$. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences are possible?

How many different code words are there such that two distinct English alphabets are followed by two distinct non-zero digits? How many of them end in an odd integer?

A class consists of $60$ boys and $40$ girls. In how many ways can a president, vice president, secretary and treasurer can be chosen, if the secretary must be a boy, the treasurer must be a girl and a student may not hold more than one office(position)?

[Enter the answer in integer]

Given $6$ flags of different colors. How many different signals can be generated by hoisting the flags on a vertical pole (one below the other), if each signal requires the use of at least $4$ flags?

How many odd numbers less than $1000$ can be formed using the digits $0, 4, 5, 7$ if repetition of digits is allowed?

How many odd numbers less than $1000$ can be formed using the digits $0, 4, 5, 7$ if repetition of digits is not allowed?