Gujarat Board Solutions for Chapter: Permutations and Combinations, Exercise 1: EXERCISE 7.1

 How many $3$-digit numbers can be formed from the digits $\mathrm{1,2},\mathrm{3,4}$ and $5$ assuming that repetition of the digits is allowed?

How many $3$-digit numbers can be formed from the digits $\mathrm{1,2},\mathrm{3,4}$ and $5$ assuming that repetition of the digits is not allowed?

How many $3$-digit even numbers can be formed from the digits $1,2,\mathrm{3,4},5,6$ if the digits can be repeated?

How many $4$-letter codes can be formed using the first $10$ letters of the English alphabet, if no letter can be repeated?

How many $5$-digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

A coin is tossed $3$ times and the outcomes are recorded. How many possible outcomes are there?

Given $5$ flags of different colours, how many different signals can be generated if each signal requires the use of $2$ flags, one below the other?