Q.1.8 - A First Course in Probability

Question

How many different letter arrangements can be made from the letters (a) Fluke? (b) Propose? (c) Mississippi? (d) Arrange? 

Step-by-Step Solution

Answer

Part(a) .different letter arrangements  for Fluke  is 120

Part(b). different letter arrangements  for Propose  is  1260

Part(c), different letter arrangements  for Mississippi  is  34650

Part(d) . different letter arrangements  for Arrange  is  1260

Step 1. Part( a) Given information

We have to find the different letter arrangements for Fluke

Step 2 , Part(a). Different letter arrangements for Fluke

 In the word Fluke   there are 5 different letters,  then the different letter arrangement for ' the word Fluke is $$\begin{gathered} 5!=5\times 4\times 3\times 2\times 1 \\ =120 \end{gathered}$$

Step 1.Part(b) . Given information

 we have to find different letter arrangements for Propose

Step 2.Part(b) . different letter arrangements for Propose

here are 7 seven letters in the word Propose,  out of letters 2 identical letters of p and o. So to get different letter arrangements for the given word we have to divide  7! by identical word arrangements 2!  and 2!. Then the different letter arrangements for the word Propose is  

$$\begin{gathered} \frac{7!}{2!2!}=\frac{7\times 6\times 5\times 4\times 3\times 2\times 1}{2\times 1\times 2\times \text{'}1} \\ =1260 \end{gathered}$$

Step 1.Part(c),Given information

Here we have to find different letter arrangements for Mississippi

Step 2.Part(c).different letter arrangements for Mississippi

In the word Mississippi, there are a total of 11 letters  out of 11, there are d identical  i letter, 4 identical s letters, and 2 identical letters p. Then to get a different word arrangement we have to divide  11! by each identical letter arrangement, thus the different letter arrangements for the word is 

$$\begin{gathered} \frac{11!}{4!\times 4!\times 2!}=\frac{11\times 10\times 9\times 8\times 7\times 6\times 5\times 4!}{4\times 3\times 2\times 1 \times 4!\times 2\times 1} \\ =34650 \end{gathered}$$

Step 1 ,Part(d). Given information

     we need to find different letter arrangements  for Arrange

Step2 Part (d). different letter arrangements for Arrange

        in this word Arrange there are a total of  7letters, in which 2 identical letters  a and 2 identical letters r   are there. To get different letter arrangements  we have to divide 7!  by identical arrangements, then the arrangements will be  

$$\begin{gathered} \frac{7!}{2!\times 2!}=\frac{7\times 6\times 5\times 4\times 3\times 2!}{1\times 2\times 2!} \\ =1260 \end{gathered}$$