In the given word $ASSASSINATION,$ there are $4\;‘S’.$ Since all the $4\;‘S’$ have to be arranged together so let as take them as one unit. The remaining letters are \[=\text{ }3\text{ }A,\text{...
In this question we get $2$ options that is (i) Either all $3$ will go Then remaining students in class are: \[25\text{ }-\text{ }3\text{ }=\text{ }22\] Number of students remained to be chosen for...
Given there are total $9\;people$ Women occupies even places that means they will be sitting on \[{{2}^{nd}},\text{ }{{4}^{th}},\text{ }{{6}^{th}}and\text{ }{{8}^{th}}\] place where as men will be...
We have a deck of cards has $4\;kings.$ The numbers of remaining cards are $52.$ Ways of selecting a king from the deck \[\Rightarrow {{~}^{4}}{{C}_{1}}=\] Ways of selecting the remaining $4\;cards$...
The student can choose $3$ questions from $part\;I$ and $5$ from $part\;II$ Or $4\;questions$ from $part\;I$ and $4$ from $part \;II$ $5$ questions from $part\;I$ and $3$ from $part \;II$
We know that there are $5$ vowels and $21$ consonants in English alphabets. Choosing two vowels out of $5$ would be done in \[^{5}{{C}_{2}}\] ways Choosing $2$ consonants out of $21$ can be done in...
The number is divisible by $10$ if the unit place has $0$ in it. The $6-digit$ number is to be formed out of which unit place is fixed as $0$ The remaining $5\;places$ can be filled by $1, \;3,\;...
In dictionary words are listed alphabetically, so to find the words Listed before $E$ should start with letter either $A,\;B, \;C \;or \;D$ But the word $EXAMINATION$ doesn`t have $B,\;C \;or \;D$...
Given at most $3\;girls$ In this case the numbers of possibilities are $0\;girl\;and\;7\;boys$ $1\;girl\;and\;6\;boys$ $2\;girl\;and\;5\;boys$ $3\;girl\;and\;4\;boys$ Number of ways to choose...
(i) Given exactly $3$ girls Total numbers of girls are $4$ Out of which $3$ are to be chosen ∴ Number of ways in which choice would be made \[\Rightarrow {{~}^{4}}{{C}_{3}}=\] Numbers of boys are...
In the word $EQUATION$ there are $5$ vowels $(A,\;E,\;I,\;O,\;U)$ and $3$ consonants $(Q,\;T,\;N)$ The numbers of ways in which $5$ vowels can be arranged are \[^{5}{{C}_{5}}\] …………… (i) Similarly,...
The word DAUGHTER has $3$ vowels $A,$ $E,$ $U$ and $5$ consonants $D,$ $G,$ $H,$ $T$ and $R.$ The three vowels can be chosen in \[^{3}{{C}_{2}}\] as only two vowels are to be chosen. Similarly, the...