Permutations an...

If $$^nC_3 + ^nC_4 > ^{n+1}C_3$$, then

If $$4.^nC_6 = 33.^{n-3}C_3$$ then $$n$$ is equal to

If $$2\times$$ $$^nC_5 = 9\times$$ $$^{n-2}C_5$$, then the value of n will be:

$$\displaystyle \sum_{r=0}^m {\;}^{n+r}C_n=$$

If $$^{15}C_{3r}=^{15}C_{r+3}$$, then the value of r is:

Let $$A=(x|x$$ is a prime number and $$x<300$$ > the number of different rational numbers, whose numerator and denominator belong to $$A$$ is:

If n and r are two positive integers such that $$n\geq r$$, then $$^nC_{r+1} + ^nC_r =$$

If $$(^{15}C_r + ^{15}C_{r-1}) (^{15}C_{15-r} + ^{15}C_{16-r}) = (^{16}C_{13})^2$$, then the value of $$r$$ is

In a game called 'odd man out', $$ m (m > 2)$$ persons toss a coin to determine who will buy refreshment for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is

Three players play a total of $$9$$ games. In each game, one person wins and the other two lose; the winner gets $$2$$ points and the losers lose $$1$$ each. The number of ways in which they can play all the $$9$$ games and finish each with a zero score is