Question

Find number of words each consisting 5 letters from letters of the word“MISSISSIPPI”
"with steps."​

Answer 1

Answer: 13

Step-by-step explanation:

Answer 2

Answer: 550.

Step-by-step explanation:

Divide and conquer this by making cases.

We got five spaces to fill, _ _ _ _ _.

with the amount of word we got in "MISSISSIPPI".

That is,

1 - M, 2 - P, 4 - I and 4 - S.

(Treat em as a group if they are alike, here you see 4 separate groups with varying amounts of letters in em)

Now in order to create letters, we first select the letters and then arrange them.

Case I : 4 alike, 1 different letters.

²C₁ × ³C₁ × $\frac{5!}{4!}$ = 30

Case II : 3 alike, 2 different letters.

²C₁ × ³C₂ × $\frac{5!}{3!}$ = 120

Case III : 3 alike, 2 alike letters.

²C₁ × ²C₁ × $\frac{5!}{3!2!}$ = 40

Case IV : 2 alike, 3 different letters.

³C₁ × ³C₃ × $\frac{5!}{2!}$ = 180

Case V : 2 alike, 2 alike, 1 different letters.

³C₂ × ³C₁ × $\frac{5!}{(2!)^{2} }$ = 180

Add em up now,

180 + 180 + 120 + 40 + 30 = 550.