Permutations and Combinations
In a library, there are m books of mathematics and n books of natural science. They can be placed on a shelf in 1209600 ways so that the books of the same subject are not separated.If m≥n. then m =
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Ten persons numbered 1,2,…..,10 play a chess tournament, each player against every other player exactly one game. It is known that no game ends in a draw. If w1,w2,…..,w10 are the number of games won by players 1,2,…..,10 respectively, and l1,l2,………….,l10 are the number of games lost by the players 1,2,…..,10 respectively, then a. ∑wi=∑li=45
b. wi+1i=9 c. ∑wl12=81+∑l12
Total number of six-digit number in which all and only odd digits appear is
a. 25(6!) b. 6! c. 21(6!) d. none of these
Evaluate (i) 8! (ii) 4!3!
If all the permutations of the letters in the word OBJECT are arranged (and numbered serially) in alphabetical order as in a dictionary, then the 717th word is
a. TOJECB b. TOEJBC c. TOCJEB d. TOJCBE
Prove that the number of ways to select n objects from 3n objects of whilch n are identical and the rest are different is 22n−1+2(n!)2(2n)!
In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, the maximum population of the city is (A) 232 (B) (32)2−1 (C) 232−1 (D) 232−1
In a three-storey building, there are four rooms on the ground floor, two on the first and two on the second floor. If the rooms are to be allotted to six persons, one person occupying one room only, the number of ways in which this can be done so that no floor remains empty is a. 8P6−2(6!)
b. 8P6 c. 8P5(6!) d. none of these
There are 10 points in a plane of which no three points are collinear and four points are concyclic. The number of different circles that can be drawn through at least three points of these points is (A) 116 (B) 120 (C) 117 (D) none of these