Question
A and B stand in a circular ring with 10 other persons.
If the arrangement of 12 persons is randomly done, the chance, that there are exactly 3 persons between A and B is A and B stand in a circular ring with 10 other persons. If the arrangement of 12 persons is randomly done, the chance, that there are exactly 3 persons between A and B isSolution
There are total 12 persons A + B + 10 others. So, total number of ways to be arranged around a circle = (12-1)!= 11! Ways Now, exactly 3 persons are to be arranged in between A and B. So, 10P3 Now, A and B can interchange their positions = 2! Ways Also, the remaining 7 can also interchange their positions with each other. So, 7! Ways So, total ways in arranging all with the condition of exactly 3 in between A and B = 2!* 10P3* 7! Ways =2*(10!/7!) *7!= 2*10! Ways So, the chance (Probability) = 2*10!/11! = 2/11 Â
22Â Â Â Â Â Â Â Â Â Â 62Â Â Â Â Â Â Â Â Â Â 178Â Â Â Â Â Â Â Â 522Â Â Â Â Â Â Â Â 1550Â Â Â Â Â Â ?
...3, 49, 191, 477, ?, 1673
3 15 35 63 99 ?
Complete the series.
19, 23, 26, 30, 33, ?
4, 8, 24, ?, 840, 9240
22 15 10 20 33 93.5
...12, 23, 68, 271, 1354, ?
3 5 15 75 1125 ?
...6   55   91   116   132    ?  . Â
12, 23, 68, 271, 1354, ?
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