Permutations and Combinations
Determine n if 2nC3:nC3=11:1
How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed?
There are 20 books on Algebra and Calculus in one library. For the greatest number of selections each of which consists of 5 books on each topic. If the possible number of Algebra books are N, then the value N/2 is __________.
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order s in an English dictionary. The number of words that appear before the word COCHIN is a.360 b. 192 c. 96 d. 48
Seven relatives of a man comprises four ladies and three gentlemen: his wife has also seven relatives-three of them are ladies and four gentlemen. In how many ways fan they invite 3 ladies and 3 gentlemen at a dinner party so that there are three man's relatives and three wife's relatives?
In how many ways can the letters of the word PERMUTATIONS be arranged if the
(i) words start with P and end with S,
(ii) vowels are all together,
(iii) there are always 4 letters between P and S?
Find the number of three-digit numbers from 100 to 999 including all numbers which have any one digit that is the average of the other two.