A teacher wants to write an ordered 4-question test from a pool of 12 questions

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Question 2229: A teacher wants to write an ordered 5-question test from a pool of 8-questions. How many different forms forms of the test can the teacher write?
How many 5-number license plates can be made using the digits 1, 2, 3, 4, 5, 6, 7 if an odd digit must come first and repetitions are allowed? not allowed?
Suppose in Exercise 2 the license number must be odd. How would it be solved?
FHow would the number of pernutations of the letters of these words be found?
1. DEED 2. COMMITTE 3. CINCINNATI 4. SATELLITE 6. MASSACHUSETTS
A player in a word game has the letters E, E, B, D, G, G , G. In how many ways can these letters be arranged?
A. 210 B. 1260 C. 840 D. 420
What is the number of permutations of six numbers on a spinner?
In how mnay ways can the 10 awimmers on an aquatic ballet team be arranged in a cirurlar pattern?

Answer by longjonsilver(2297)

   (Show Source):

You can put this solution on YOUR website!
if the teacher wants all possibilities of 5 questions, even if repeated (just in different order) eg 12345 and 12354 are 2 different versions, then use permutations:
n=8, r=5, so we get

...8!/3! = 6720 different combinations of the 8 questions.
If however, the teacher wants all the combinations of 5 questions where 12345 and 12354 etc are considered the same, then there are 6720/5! = 56.
2a. odd digit first...4 possibilities,
so 4 then 7 then 7 then 7 then 7 possibilities with repetitions = 9604
2b. with repetitions not allowed....
we have 4 then 6 then 5 then 4 then 3 = 1440.
3. if number plate was to be odd, its last digit would have to be 1,3,5 or 7, so work that out .
Jon