Hello everyone, i'm having some issues on this problem: A coin is tossed ten times. In each case the outcome H (for heads) or T (for tails) is recorded. (One possible outcome of the ten tossings is denoted THHTTTHTTH.) I got a, d right i believe. but I need someone to check if i did the others ones right. a. what is the total number of possible outcomes of the coin-tossing experiemnt? I said: 2^10 = 1,024 b. In how many of the possible outcomes are exactly 5 heads obtained? [# of outcomes with exactly 5 heads] = [total # of outcomes] - (10 choose 5) This one I'm not sure what i'm suppose to do, when i say 10 choose 5, i mean you have a set of 10, and i'm wanting to choose 5 elements out of that set that are H but i'm not sure how to represeent this... c. In how many of the possible outcomes is at least 8 heads obtained? For this one would i do: [# of outcomes with at least 8 heads obtained] = [total number of outcomes] - [number of outcomes that contain 8 heads] = 1024 - (10 choose 8) = 1024 - 10!/[8!(2!)] = 1024 - 45 = 979 d. In how many of the possible outcomes is at least one head obtained? [# of outcomes w/ at least 1 head] = [total # of outcomes] - [# of outcomes with no heads] = 1024 - 1 = 1023. e. In how many of the possible outcomes is at most one head obtained? I think i got this one, but the # of outcomes with 1 head i might have got wrong. [# of outcomes with at most 1 head] = [# of outcomes with no heads] + [# outcomes with 1 head] = 1 + (10 choose 1) = 1 + 10!/[1!(10-1)!] = 1 + 10!/9! = 11 Any help would be great, i'm having issues figuring out how to choose once i figure out the method it seems.