Out of different alphabets consisting of different consonants and different vowels, how many arrangements can be made which consist of consonants and vowels ?
cases are refered to the upper court to challenge the decisions given by the lower court If majority of the decisions are changed from these cases, find the number of ways of doing so
There are black, red and blue pens in a box In how many ways can pens be selected from it such that
$(i)$ Both the pens are of same colour?
$(ii)$ Both the pens are of different colours?
In how many ways can a group of members be formed from teachers, boys and girls for an adventure activity so that it includes teachers and at the most girl ?
A Kabaddi match is played on a ground between two countries $A$ and $B$ Among persons inquired from the spectators, spectators favoured country A and the rest favoured country $B$ In how many ways can spectators be selected from these spectators so as to included majority spectators favouring country $A$?
Three pairs (Boy-Girl) are gathered from three schools for a Tennis-doubles competition Two players are selcted from them In how many ways can it be done such that it includes
$(i)$ a boy and a girl ?
$(ii)$ a boy and a girl but not from the same school ?
There are chocolates of company $A$, chocolates of company $B$ and chocolates of company $C$ in a display refrigerator Tanya selects chocolates from it In how many ways can she select at least chocolates of company $B$ ?
teachers, boys, girls and a principal are to be arranged in a row for a group photo In how many ways can it be done so that chairs each on both the ends are occupied only by boys, girls are not in the adjacent seats and the principal must be seated exactly in the centre ?
What is the rank of the word $NATURE$, if all arrangements are made using all letters of the word $NATURE$ and arranged according to dictionary order ?
In how many ways can cars of different models of company $A$ and cars of different models of company $B$ be parked in a row in a parking plot, so that cars of both the companies are parked alternately ?