Question 1048905
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(1) How many ways can 20 objects be arranged into groups of 5? (order does not matter)

(2) A test has five true-false questions that a student does not know how to answer. What is the probability that student will get all five questions to correct?

(3) How many ways are there to arrange 5 people in 3 seats?
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<pre>
(1) {{{C[20]^5}}} = {{{20!/(15!*5!)}}} = {{{(20*19*18*17*16)/(1*2*3*4*5)}}} = 15504 ways.

   The number of combinations of 20 objects taken 5 at a time.

   See the lessons 
   &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>

   &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>

   &nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>
   in this site.


(2)  {{{1/2^5}}} = {{{1/32}}}.



(3)  5*4*3 = 60 ways.
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