Hi, I don't understand the solution approach for this problem:
In how many ways can 11# signs and 8* signs be arranged in a row so that no two * signs come together
Answer = [spoiler]12C4=495[/spoiler]
After searching several sites this is the only explanation offered:
Arrange the 11 # signs. Now we have 12 slots (10 slots between # signs and 2 on the extremes). Given that the # signs as well as the * signs are identical, we have 12C8 arrangements.
It's clear that finding the number of ways there are two spaces between every # sign is logicial, because when you assign the 8 * signs to this number you have the solution.
What i don't get is HOW you find the number of ways there are two spaces between every #. From where does the number 10 and 2 in the solution proposal come frome? Please give a thourough explanation.
Thanks
In how many ways can 11# signs and 8* signs be arranged in a row so that no two * signs come together
Answer = [spoiler]12C4=495[/spoiler]
After searching several sites this is the only explanation offered:
Arrange the 11 # signs. Now we have 12 slots (10 slots between # signs and 2 on the extremes). Given that the # signs as well as the * signs are identical, we have 12C8 arrangements.
It's clear that finding the number of ways there are two spaces between every # sign is logicial, because when you assign the 8 * signs to this number you have the solution.
What i don't get is HOW you find the number of ways there are two spaces between every #. From where does the number 10 and 2 in the solution proposal come frome? Please give a thourough explanation.
Thanks
