Consider reordering the letters in the word TENNESSEE. Use the technique shown in Example 9.5.11 to answer the following questions. (a) If the N's are placed first, how many ways are there to choose positions for them? 21 x If the E's are placed second, how many ways are there to choose positions for them? 5 x If the S's are placed third, how many ways are there to choose positions for them? 21 X If the T is placed fourth, how many ways are there to choose a position for it? 8 X So, the total number of ways to reorder the letters in the word TENNESSEE is 84 (b) Imagine placing the letters into positions in a different order. If the E's are placed first, how many ways are there to choose positions for them? 126 If the T is placed second, how many ways are there to choose a position for it? 8 x If the S's are placed third, how many ways are there to choose positions for them? 7 X If the N's are placed fourth, how many ways are there to choose positions for them? 6 x x. (c) When the method suggested in part (b) is used to find the total number of ways to reorder the letters in the word TENNESSEE, the result is the same as B✔ when the method of part (a) is used.
Consider reordering the letters in the word TENNESSEE. Use the technique shown in Example 9.5.11 to answer the following questions. (a) If the N's are placed first, how many ways are there to choose positions for them? 21 x If the E's are placed second, how many ways are there to choose positions for them? 5 x If the S's are placed third, how many ways are there to choose positions for them? 21 X If the T is placed fourth, how many ways are there to choose a position for it? 8 X So, the total number of ways to reorder the letters in the word TENNESSEE is 84 (b) Imagine placing the letters into positions in a different order. If the E's are placed first, how many ways are there to choose positions for them? 126 If the T is placed second, how many ways are there to choose a position for it? 8 x If the S's are placed third, how many ways are there to choose positions for them? 7 X If the N's are placed fourth, how many ways are there to choose positions for them? 6 x x. (c) When the method suggested in part (b) is used to find the total number of ways to reorder the letters in the word TENNESSEE, the result is the same as B✔ when the method of part (a) is used.
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 4SE: Answer the following questions. 4. Describe how the permutation of ii objects differs from the...
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Transcribed Image Text:Consider reordering the letters in the word TENNESSEE. Use the technique shown in Example 9.5.11 to answer the following questions.
(a) If the N's are placed first, how many ways are there to choose positions for them?
21
X
If the E's are placed second, how many ways are there to choose positions for them?
5
X
If the S's are placed third, how many ways are there to choose positions for them?
21
X
If the T is placed fourth, how many ways are there to choose a position for it?
8
X
So, the total number of ways to reorder the letters in the word TENNESSEE is 84
(b) Imagine placing the letters into positions in a different order.
If the E's are placed first, how many ways are there to choose positions for them?
126
If the T is placed second, how many ways are there to choose a position for it?
8
X
If the S's are placed third, how many ways are there to choose positions for them?
7
X
If the N's are placed fourth, how many ways are there to choose positions for them?
6
X
x.
(c) When the method suggested in part (b) is used to find the total number of ways to reorder the letters in the word TENNESSEE, the result is the same as
↑
when the method of part (a) is used.
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