In how many ways can a girl and a boy be selected from a group of $15$ boys and $8 $ girls
$15 \times 8$
$15 + 8$
$^{23}{P_2}$
$^{23}{C_2}$
If all the letters of the word $'GANGARAM'$ be arranged, then number of words in which exactly two vowels are together but no two $'G'$ occur together is-
There are $3$ sections in a question paper and each section contains $5$ questions. A candidate has to answer a total of $5$ questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is
The value of $\sum\limits_{r = 0}^{n - 1} {\frac{{^n{C_r}}}{{^n{C_r} + {\,^n}{C_{r + 1}}}}} $ equals
How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number
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?