Final questions (1 Viewer)

[allGenreGamer]

I have two more quick questions:

1. Six people, of whom A and B are two, arrange themselves at random in a row. What's the probability that there're at least 3 people between A and B?
(Answer: 1/2)

2. (n-1)C(k-1) + (n-1)C(k)

(Answer: nCk)

Thanks in advance. Test is in 2 days, so plz help with my final questions!

 

[Affinity]

I believe the answer for the first question is 1/5
choose the 2 spots for A and B such that the condition is satisfied:
they can be:
(1,5), (1,6), (2,6) -> 3 cases

and to choose the 2 spots in general there are (6 C 2) = 15 ways

so the probability should be 1/5

the second question is just pascal's triangle's relationship..

you could do it by:

consider the equation:

(1+x)^n = (1+x)^(n-1) + x(1+x)^(n-1)

and the coefficient of x^k on both sides.

or you could do it by expanding the binomial coefficients and reducing.