Permutations and Combinations
If N denotes the number of ways of selecting r objects of out of n distinct objects (r≥n) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .r−1Cr−n b. .r−1Cn c. .r−1Cn−1 d. none of these
Number of ways in which 200 people can be divided in 100 couples is a. 2100(100!)(200)! b. 1×3×5××199 c. (2101)(2102)………….(2200) d. (100)!(200)!
Statement 1: the number of ways of writing 1400 as a product of two positive integers is 12. Statement 2: 1400 is divisible by exactly three prime factors.
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
There are 2n guests at a dinner party. Supposing that eh master and mistress of the house have fixed seats opposite one another and that there are two specified guests who must not be placed next to one another, show that the number of ways in which the company can be placed is (2n−2)!×(4n2−6n+4)˙
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
Total number less than 3×108 and can be formed using the digits 1, 2, 3 is equal to a. 21(39+4×368) b. 21(39−3) c. 21(7×38−3) d. 21(39−3+38)