Question

how many different words containing all the letter of the word SOCIETY can be formed such that vowels never occur together​

Answer 1

Answer:

Step-by-step explanation:

count four vowels. o, i, e, y.

But let’s say we’re ignoring the y to make you happy.

There are a couple of different ways the three vowels can come together. Either they’re all together as 1–3, 2–4, 3–5, 4–6 or 5–7.

The chances that eio are the first three letters is 3/7*2/6*1/5. Since it’s equally likely that eio are the first three letters as it is that they’re located anywhere else, and there are five “slots” altogether we multiply this by 5.

So the chances that eio are together anywhere is 3/7*2/6*1/5*5 = 3/7*2/6 = 1/7.

The chances of that not happening is 1-(1/7), or 6/7.