a) Given that 3 people out of 6 are to be together, we consider tham as 1 group and so we are left with 3 other people - so 4 groups. Total ways to arrange them
= 4! * Number of permutations of those 3 people together
= 4! * 3!
= 144
Therefore there are 144 ways to arrange here.
b) Given that 2 people refuse to be together, total ways to place the people here is computed as:
= Total ways to arrange rest 4 people * Total ways to arrange those 2 people in 5 positions after 4 people are arranged
= 4! * 5*4
= 480
Therefore there are 480 ways to arrange here.
2. Suppose 6 people will be lined up to get on a bus. Find the number...
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