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Model Paper 8 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 83 Marks
Question
In how many ways can six persons be seated in a row?
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Answer

Given: Six persons are to be arranged in a row.
Assume six seats, now in the first seat, any one of six members can be seated, so the total number of possibilities is 6 Similarly, in the second seat, any one of five members can be seated, so the total number of possibilities is ${ }^5 C _1$ In the third seat, any one of four members can be seated, so the total number of possibilities is ${ }^4 C _1$
In the fourth seat, any one of three members can be seated, so the total number of possibilities is ${ }^3 C _1$
In the fifth seat, any one of two members can be seated, so the total number of possibilities is ${ }^2 C _1$
In the sixth seat, only one remaining person can be seated, so the total number of possibilities is ${ }^1 C _1$
Hence the total number of possible outcomes $={ }^6 C _1 \times{ }^5 C _1 \times{ }^4 C _1 \times{ }^3 C _1 \times{ }^2 C _1 \times{ }^1 C _1=6 \times 5 \times 4 \times 3 \times 2 \times 1=720$

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