Permutations and Combinations
A meeting is to be addressed by 5 speakers A, B, C, D, E. In how many ways can the speakers be ordered, if B must not precede A (immediately or otherwise)?
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Evaluate (i) 8! (ii) 4!3!
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 __________.
Find the number of arrangements of the letters of the INDEPENDENCE. In how many of these arrangements,(i) do the words start with P(ii) do all the vowels always occur together(iii) do the vowels never occur together(iv) do the words begin with I and end in P?
Statement 1: number of ways in which 10 identical toys can be distributed among three students if each receives at least two toys is 6C2˙
Statement 2: Number of positive integral solutions of x+y+z+w=7is6C3˙
The number of four-digit numbers that can be made with the digits 1, 2, 3, 4, and 5 in which at least two digits are identical is
a. 45−5! b. 505 c. 600 d. none of these
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?
How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4; 5 if the digits can be repeated?
There are n points in a plane in which no three are in a straight line except m which are all in a straight line. Find the number of (i) different straight lines, (ii) different triangles, (iii) different quadrilaterals that can be formed with the given points as vertices.