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How many ways can a student select 7 questions from an exam containing 11 questions if he must answer the last question?
If he must answer the last question, he effectively needs to select 6 from 10. This can be done in 10C6 = 10*9*8*7/(4*3*2*1) = 210 ways.
How many ways can a student select 5 questions from an exam containing twelve questions if he must select the last question?
If he must include the last question, then his choices really boil down tohow many ways he can select 4 more from the remaining 11.The number of ways he can select 4 from 11 is (11 x 10 x 9 x 8) = 7,920 ways .But each group of 4 can be selected in 24 different ways.So he can only wind up with 7920/24 = 330 different groups of questions.
How many ways can 10 stand in a line?
10 people can line up in (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) = 3,628,800 different ways.
In how many ways can you arrange of the letter PHILIPPINES?
Assuming the Ps and Is are indistinguishable: There are 10! / 3! / 3! = 100800 ways If the Ps and Is are distinguishable, then there are 10! = 3628800 ways
How many ways are there to make 45 cents out of 15 10 5?
There are 13 ways.
