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January 31st, 2017, 05:48 PM  #1 
Newbie Joined: Jan 2017 From: San angelo Posts: 1 Thanks: 0  can I please get help on how to work out something like this
Consider the set {a, b, c, d, e}. (a) How many sequences of length 5 can you form from these elements? (Remember, repeated elements are okay in sequences.) (b) How many sequences of length 5 can you form from these elements if the second element of the sequence must be d? (c) How many sequences of length 5 can you form from these elements if the first element of the sequence must be c and the last element must be a vowel? 2. How many distinct 6digit positive numbers are there whose third digit is 2? 
January 31st, 2017, 05:53 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,268 Thanks: 2434 Math Focus: Mainly analysis and algebra 
Count how many ways there are to select each element of the sequence and multiply.

January 31st, 2017, 06:36 PM  #3 
Senior Member Joined: May 2016 From: USA Posts: 991 Thanks: 406 
With respect to question a, how many distinct sequences can you get if every element is the same? How about if every element but one is the same? Let's work that last question out. There are five distinct ways that the four like elements can be chosen. Given that, there are four ways that the unlike element can be chosen. And there are five positions that the unlike element can be in. So the answer to the question of how many distinct sequences contain four like elements and one unlike element is 5 * 4 * 5 = 100. Of course there are other possibilities. You might have five unlike elements. How many distinct sequences are possible in that case? Figure out what all the possible cases are, and then compute how many distinct sequences are covered by each case, and add those numbers up. Last edited by JeffM1; January 31st, 2017 at 06:38 PM. 

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