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Question
The next number in the sequence 3,6, 11, 18, 27 , ---
34
36
38
40
ANSWER : 3
Descrption
12 marbles are selected at random form a large collection of white , red, green and yellow marbles . The number of marbles of each color is unlimited. Find the probability that the selection contains at least one marble of each color ? This is same as W + R + G + Y = 12, where all are positive integers. <br/> Step I.. <br/> first, give one to each, hence 4 gone. Now you can distribute the remaining 8 to anyone as the restriction of at least one is done.. W + R + G + Y = 8..W + R + G + Y = 8.. Now, take this as 8 marbles and 3 partitions, so total 11 things. You can choose these 3 partitions in 11C3 ways = 11!/8!3! = 11∗10∗9/3∗2 = 11∗5∗3 Step II.. <br/> Total ways.. <br/> W + R + G + Y = 12 <br/> Now, take this as 12 marbles and 3 partitions, so total 15 things. You can choose these 3 partitions in 15C3 ways = 15!/12!3! = 15∗14∗13/3∗2 = 5∗7∗13 <br/> Probability = 11∗5∗3/5∗7∗13 = 33/91
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