SOLVED:If you flip a coin 10 times, you get a sequence of Heads (H) and tails (T). (a) How many different sequences of heads and tails are possible? (b)How many different sequences of heads and tails

Video Transcript

In this interrogate were given a coin disconnected 10 times. Hence there is a sequence of heads and tails and the event which denotes ahead and the event T denotes a chase In contribution A. We want to find the number of potential different sequences of lead and tail. I ‘m going to draw 10 slots here. Each slot here represents a flip. so in the first toss we can get either heads or tails. So there ‘s two ways and now end in combinatorics is terms or is plus then and thus there ‘s times in the second toss we can get either heads or tails. So there ‘s two ways and the third course besides two ways, heads or tails. so two ways so on and so forth. All the way to the last convulse or the last wow. Final convulse here. besides two ways of either hate of you. So the answer will be two to the power of 10 since it ‘s two times two times two, 10 times. So That is 10, 2, 4 ways in B. We want to find the number of potential different sequence of heads and tails that have precisely five heads. So we ‘re looking at five heads here And the remaining will be five tails. No, You see that there are actually 10 tosses. So That will be 10 factorial way of getting the Arranging 10 tosses. But since five heads here are repeats and five buttocks here are repeats, you need to divide by the five factorial way of the five hits And the five factorial for the five tails. And so The answer will be two, now in separate C we want to find the number of potential sequence that have at most two heads. So this can be split into three mutually single font. The first case is zero head, All all is plus one head or two hits. now for zero head means they are all going to be tails. So there ‘s only one way, it ‘s barely 10 tables, so there ‘s only one way for one head. That means there ‘s one head and nine buttocks. indeed again There is 10 factorial ways of arranging this. Um 10 symbols but divided by nine repeats for buttocks. thus divided by nine factorial. nowadays for two heads It would be again 10 factorial manner of arranging these 10 symbols Divided by two factorial. This for two heads that are repeats and 48 Tales that are repeat. so divided by eight Victoria. And indeed the answer is 56.

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