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How many ways can 9 books be arranged on a shelf so that 5 of the books are always together?
You can simplify the problem by considering it as two different problems. The first involves consider the five-book chunk as a single book, and calculating the permutations there. The second involves the permutations of the books within the five-book block. Multiplying these together gives you the total permutations. Permutations of five objects is 5!, five gives 5!, so the total permutations are: 5!5! = 5*5*4*4*3*3*2*2 = 263252 = 14,400 permutations
How many ways can five differently colored marbles be arrange in a row?
They can be arranged 5! or 120 ways.
What is the probability that the birthdays of five persons chosen at random will fall in twelve different calendar months?
The probability that the birthdays of five persons chosen at random will fall in twelve different calender months is zero. You would need at least twelve persons to have a non zero probability.
How many combinations are there for a 5 digit code using 3 2s and 2 4s?
There are five digits all together. The number of ways of arranging them is5 x 4 x 3 x 2 x 1 = 120 .But the three 2s can be arranged in 3 x 2 = 6 different ways and they all look the same.And the two 4s can be arranged in 2 different ways and they look the same.So out of the 120 different ways of arranging all five, there's a group of sixfor every possible arrangement of the 2s that all look the same, and there'sa group of two for each possible arrangement of the 4s that both look thesame.The number of combinations that look different is 120/(6 x 2) = 10 .And here they are:2 2 2 4 42 2 4 2 42 2 4 4 22 4 2 2 42 4 2 4 22 4 4 2 24 2 2 2 44 2 2 4 24 2 4 2 24 4 2 2 2
How many different three member committees can be formed from a group of twenty-five people?
There are 2300 possible combinations.
