Abhijit Guha Solutions for Chapter: Permutation and Combination, Exercise 2: Practice Problems Level 2

A telegraph has five arms and each arm is capable of three distinct positions, including the position of rest. What is the total number of signals that can be made?

In a city $M$, the license plates consist of $3$ letters consisting of consonants only. Any two license plates will be the same only if consists of the same $3$ letters in the same order. How many license plates are possible if the letter $M$ cannot occur as the last character and can occur only when the letter is immediately after it is $T$?

A person has $12$ notes of $\mathrm{Rs} 50$ each, $9$ notes of $\mathrm{Rs} 20$ each, $5$ notes of $\mathrm{Rs} 10$ each and $4$ notes of $\mathrm{Rs} 5$ each. In how many different ways can be contribute to a Puja committee?

There are four teams in each of the four groups $A, B, C$, and $D$. Every team in each group will play with each other once. The top teams from each will go to the next round and so on the top $2$ teams will play final. The minimum number of matches played will be:

In how many ways can the letters of the English alphabet be arranged so that there are eight letters between $Y$ and $Z$, and no letters is repeated?

A staircase contains $12$ steps, can climb it $1$ or $2$ steps. But $8^{\mathrm{th}}$ step contains a big break so one cannot step on it. In how many ways can one reach the top?

In how many ways can $n$ women be seated in a row so that a particular women will not be next to each other?

Each of the two friends has $10$ cadbury chocolates and $6$ pancakes. A fair exchange is such they exchange a cadbury chocolate for a cad bury chocolate or a pancake for a pancake. How many ways there are to carry out one fair exchange between these two friends?