Question

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

Short 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-by-step solution

Step 1. Part( a) Given information

We have to find the different letter arrangements for Fluke

, 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

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

,Part(d). Given information

we need to find different letter arrangements for Arrange

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

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