Permutations and Combinations
m men and n women are to be seated in a row so that no two women sit together. If m>n, then the number of ways in which they can be seated is
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Let there be n≥3
circles in a plane. The value of n
for which the number of radical centers is equal to the number of radical axes is (assume that all radical axes and radical centers exist and are different).
a. 7 b. 6 c. 5 d. none of these
In a room there are 12 bulbs of the same wattage, each having separate switch. The number of ways to light the room with different amounts of illumination is (a)122−1 (b) 212 (c) 212−1 (d) none of these
A batsman scores exactly a century by hitting fours and sixes in 20 consecutive balls. In how many different ways can he do it if some balls may not yield runs and the order of boundaries and over boundaries are taken into account?
Find the number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, what will be the 50th word?
10 different letters of an alphabet are given. Words with 5 letters are formed from these given letters then the numbers of words which have atleast one letter represent is:
Evaluate (n−r)!n!, when (i) n=6,r=2 (ii) n=9,r=5
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, 10 passengers enter the train during the journey with 10 different ticket of two class. The number of different sets of tickets they may have is
d. none of these