How many words, with or without meaning, can be formed using all the letters of the word $\mathrm{EQUATION}$ at a time so that the vowels and consonants occur together?
How many words, with or without meaning, can be formed using all the letters of the word $\mathrm{EQUATION}$ at a time so that the vowels and consonants occur together?
In the word $EQUATION$, there are $5$ vowels, namely, $A , E , I , O$ and $U$ and $3$ consonants, namely $Q , T$ and $N.$
since all the vowels and consonants have to occur together, both $(AEIOU)$ and $(QTN)$ can be assumed as single objects. Then, the permutations of these $2$ objects taken all at a time are counted.
This number would be $^{2} P_{2}=2 !$
Corresponding to each of these permutations, there are $5 !$ Permutations of the five vowels taken all at a time and $3 !$ Permutations of the $3$ consonants taken all at a time.
Hence, by multiplication principle, required number of words $2! \times 5! \times 3!=1440$
Similar Questions
Let $n(A) = 3, \,n(B) = 3$ (where $n(S)$ denotes number of elements in set $S$), then number of subsets of $(A \times B)$ having odd number of elements, is-
Let $n(A) = 3, \,n(B) = 3$ (where $n(S)$ denotes number of elements in set $S$), then number of subsets of $(A \times B)$ having odd number of elements, is-
What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these
two are red cards and two are black cards,
What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these
two are red cards and two are black cards,
$\mathop \sum \limits_{0 \le i < j \le n} i\left( \begin{array}{l}
n\\
j
\end{array} \right)$ is equal to
$\mathop \sum \limits_{0 \le i < j \le n} i\left( \begin{array}{l}
n\\
j
\end{array} \right)$ is equal to
If $n = ^mC_2,$ then the value of $^n{C_2}$ is given by
If $n = ^mC_2,$ then the value of $^n{C_2}$ is given by
- [AIEEE 2012]
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw
- [IIT 1986]