# Permutations and Combinations, Probability

Let F be be mini 4X4 chessboard => it has 16 fields in all. In how many ways is it possible to select two fields of F such that the midpoint of the segment joining the centres of the two fields should also be the centre of a field?

Varun has to call his friend Amar, but he doesn't remember Amar's phone number. He has two options, first to try calling Amar directly and in case he doesn't get the number right he could try the second option of calling up Vineet, another friend of his who would in turn give cosmic_glitch's number of who finally give him Amar's number. Alternatively, Varun can try the second option first. Given Varun needs to minimize the total number of calls he has to make, what should be the minimum level of certainity that Varun should have regarding the number he already has so that it would be advisable for him to try the first option before the second?

Varun has to call his friend Amar, but he doesn't remember Amar's phone number. He has two options, first to try calling Amar directly and in case he doesn't get the number right he could try the second option of calling up Vineet, another friend of his who would in turn give cosmic_glitch's number of who finally give him Amar's number. Alternatively, Varun can try the second option first. Given Varun needs to minimize the total number of calls he has to make, what should be the minimum level of certainity that Varun should have regarding the number he already has so that it would be advisable for him to try the first option before the second?

Varun has to call his friend Amar, but he doesn't remember Amar's phone number. He has two options, first to try calling Amar directly and in case he doesn't get the number right he could try the second option of calling up Vineet, another friend of his who would in turn give cosmic_glitch's number of who finally give him Amar's number. Alternatively, Varun can try the second option first. Given Varun needs to minimize the total number of calls he has to make, what should be the minimum level of certainity that Varun should have regarding the number he already has so that it would be advisable for him to try the first option before the second?

 What are the number of ways, when ten persons, amongst whom A, B and C are to speak at a function, where A wants to speak before B and B wants to speak before C?

• (factorial 10)/6
• (factorial 10)/3
• 10P3 * factorial 7
• factorial 3 * factorial 7

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In how many ways 25 balls can be selected from a bag containing 15 identical red balls, 20 identical green balls and 25 identical yellow balls?

• 291
• 265
• 281
• 300

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In how many ways can u divide 30 identical chocolates amongst 4 people A B C D such that A>B>C??

probability of passing in physics maths and chem is p,m,c respectively

student has 75 percent chance in passing atleast one ,50 percent chance in passing atleast two and 40 percent chance in passing exactly 2 …thenn which relation is true

plz put explanation too

• p+m+c =19/20
• p+m+c =27/20
• pmc=1/10
• pmc=1/4

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Q. The probablity of a bomb hitting bridge is 0.5 and two direct hits are required to destroy it. Find the least number of boms required so that probablity of the bridge being destroyed is 0.9
• 8
• 9
• 10
• 11

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The Number of Positive numbers of not more than 10 digits formed by 0,1,2 and 3 is.

• 4^10-1
• 18
• 24
• 4^10-3^10

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find the number of natural number solution to the equation a+b+c

• 12C3
• 11C2
• 13C3
• 13C2

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n things (each thing belonging to a particular place ) have to be distributed in n places so that no particular thing is arranged its correct place.
Plz provide the logic for the formula .... ?

• n!-n!/1! + n!/2! …

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Ten books are arranged in a row on a bookshelf. A student has to select three out of these ten books in such a way that no two books selected by him must have been lying adjacently. In how many ways can he make the selection?

• 72
• none of these
• 56
• 64

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An urn contain 9 blue, 7 white and 4 black balls. If 2 balls are drawn at random, then what is the probability that only one ball is white ?

• 91/190
• 121/190
• 71/190
• 93/190
• None of these

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In a test consisting of 15 questions, 3 marks are awarded for a correct answer, 1 mark is deducted for an incorrect answer and no mark is awarded for an unattempted question. If a student attempts at least one question in the paper, what is the number of distinct scores that he can get?

• 58
• 57
• 59
• None of These

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in how many ways "THERAPY" can be arranged so that the vowels never come together

• 211
• 720
• 5040
• 4998

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The crew of an 8 member rowing team is to be chosen fom 12 men, of which 3 must row on one side only and 2 must row on the other side only. Find the number of ways of arranging the crew with 4 members on each side.

• 30240
• 40320
• 10080
• None of these
• 60480

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In an examination the maximum marks for each of the three papers is 50 each. The maximum marks for the fourth paper is 100. Find the number of ways with which a student can score 60% marks in aggregate.

• 220800
• 330850
• 233551
• 110551
• none of these

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In class X final examination, 70 students got distinction in science, 83 in Math's, 51 in social studies and 35 in English. Three students got distinction in all the subjects. 5 got distinction in science, social studies and maths only. Three got distinction in social studies, Maths and English only. Two got distinction in science, social studies and English only, 15 got distinction in science and social studies. If the distinction in observed only in these mentioned pairs and triplets, then find the number of students getting distinction in at least one of the given subjects?

• 140
• 195
• 160
• 200

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Seven different objects must be divided among three people. In how many ways can this be done if one or two of them must get no objects?

• 36
• 174
• 84
• 381
• 180

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