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PARAGRAPH A There are five students S1,\...

PARAGRAPH A There are five students `S_1,\ S_2,\ S_3,\ S_4` and `S_5` in a music class and for them there are five seats `R_1,\ R_2,\ R_3,\ R_4` and `R_5` arranged in a row, where initially the seat `R_i` is allotted to the student `S_i ,\ i=1,\ 2,\ 3,\ 4,\ 5` . But, on the examination day, the five students are randomly allotted five seats. For `i=1,\ 2,\ 3,\ 4,` let `T_i` denote the event that the students `S_i` and `S_(i+1)` do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event `T_1nnT_2nnT_3nnT_4` is `1/(15)` (b) `1/(10)` (c) `7/(60)` (d) `1/5`

A

`(1)/(15)`

B

`(1)/(10)`

C

`(7)/(60)`

D

`(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
Event `T_(1)nn T_(2) nn T_(3) nn T_(4)`: No two students with consecutive index sit adjacent.
So, we have following possible arrangements:
13524, 14253
24135, 24153, 25314
31425, 31524, 35142, 35241
41352, 42531, 42513
52413, 53142 ltgtbrgt Thus, favorable cases = 14
Hence, required probability = `(14)/(120) = (7)/(60)`
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