$^n{P_r}{ \div ^n}{C_r}$ =
$n\,!$
$(n - r)!$
$\frac{1}{{r!}}$
$r\,!$
(d)On simplification you get required result.
If $^{43}{C_{r – 6}} = {\,^{43}}{C_{3r + 1}},$ then the value of $r$ is
The English alphabet has $5$ vowels and $21$ consonants. How many words with two different vowels and $2$ different consonants can be formed from the alphabet?
In how many ways can a student choose a programme of $5$ courses if $9$ courses are available and $2$ specific courses are compulsory for every student?
The number of ways in which thirty five apples can be distributed among $3$ boys so that each can have any number of apples, is
The number of words (with or without meaning) that can be formed from all the letters of the word $"LETTER"$ in which vowels never come together is
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