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How many ways can five differently colored marbles be arrange in a row?
They can be arranged 5! or 120 ways.
It is required to seat 5 men and 4 women in a row so that the women occupy the even places how many such arrangements are possible?
There are two ways to look at this problem; gender or person. Gender (M=Male, F=Female); There is only one way and that is MFMFMFMFM. By person, you have 9 places to fill. The first is 5 males could be placed there, the next 4 females could be placed there, the next 4 males can be placed there, the next 3 females can be placed there and so forth. So in this instance there are 5*4*4*3*3*2*2*1*1 = 2880 arrangements. Another way is just 5!*4!=2880. Here 5! is for men and 4! for women. ie. Men can be arranged in 5 ways and women can be arranged in 4 ways.
How do you you arrange 3 quarters 4 dimes and 2 nickels that are indistinguishable in a row?
Any way you like!
How many ways can you arrange 36 squares in equal rows?
Oh, dude, arranging 36 squares in equal rows? That's like asking how many ways you can arrange your socks in a drawer. Technically, you can arrange them in 36! ways, which is a super big number that I'm too lazy to calculate. So yeah, have fun with your square arranging adventures!
How many different ways can 8 computer operators be seated in row?
The number of different ways that 8 computer operators can be seated in a row is the same as the number of permutations of 8 things taken 8 at a time. That is 8 factorial, which is 40,320. Think of it this way... You have 8 choices for the first seat, 7 choices for the second seat, 6 choices for the third seat, and so on to 1 choice for the last seat. That is 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1, otherwise known as 8 factorial.
