Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: WBJEE 2020

In a certain test, there are $n$ questions. In this test $2^{n-i}$ students gave wrong answers to at least $i$ questions, where $i=1,2,\dots ,n$. If the total number of wrong answers given is $2047$, then $n$ is equal to

In a $12$ storied building, $3$ persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?

A candidate is required to answer $6$ out of $12$ questions which are divided into two parts $A$ and $B,$ each containing $6$ questions and he/she is not permitted to attempt more than $4$ questions from any part. In how many different ways can he/she make up his/her choice of $6$ questions?

The number of selection of $n$ objects from $2n$ objects of which $n$ are identical and the rest are different, is

From a collection of $20$ consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is

On the occasion of Dipawali festival each student of a class sends greeting cards to others. If there are $20$ students in the class, then the total number of greeting cards exchanged by the students is

There are $7$ greeting cards, each of a different colour and $7$ envelopes of same $7$ colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly $4$ of the cards go into envelopes of respective colour is,