Permutations and Combinations
Sonia decides to hang 6 different potted plants in a row in her shop. The money plant is to be hung at either end of the row. Find the number of different arrangements possible.
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How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?
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)
A five-digit number divisible by 3 is to be formed using the digits 0,1,2,3,4,and5, without repetition. The total number of ways this can done is (a) 216 (b) 240 (c) 600 (d) 3125
Number of ways in which three numbers in A.P. can be selected from 1,2,3,…,n is a. (2n−1)2 if n is even b. n4n−2 if n is even c. 4(n−1)2 if n is odd d. none of these
A number of 18 guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?
Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that(i) all vowels occur together (ii) all vowels do not occur together.
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?