Question

lesson 19.2 checkpoint
once you have completed the above problems and checked your solutions, complete the lesson checkpoint
below.
complete the lesson reflection above by circling your current understanding of the learning goal.

1. jane has 10 cards. jane is going to make a row containing 4 cards. how many unique ways can she

order the row?
a. 5040
b. 151200
c. 210

1. if all the letters in the word envelope are randomly rearranged, what is the probability the letters will spe

the word envelope?
a. \\( \frac { 3 } { 28 } \\)
b. \\( \frac { 1 } { 720 } \\)
c. \\( \frac { 1 } { 1120 } \\)
d. \\( \frac { 1 } { 6720 } \\)

Explanation:

Step1: Calculate permutations for the first problem

The formula for permutations is \(P(n,r)=\frac{n!}{(n - r)!}\). Here \(n = 10\) and \(r=4\).

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Step2: Calculate probability for the second problem

The word "ENVELOPE" has 8 letters. But there are 3 'E's. The number of permutations of \(n\) objects with \(n_1\) of one kind is \(\frac{n!}{n_1!}\). So the number of permutations of "ENVELOPE" is \(\frac{8!}{3!}=\frac{8\times7\times6\times5\times4\times3!}{3!}=6720\). There is only 1 correct arrangement. So the probability is \(\frac{1}{6720}\).

Answer:

1. A. 5040
2. D. \(\frac{1}{6720}\)