Hello! Sadly i am struggling with these few problems... They are a bit confusing

Question

Hello! Sadly i am struggling with these few problems... They are a bit confusing and I cannot get to solve them fully. Help solving them would would be great.

Thank you very much

THREE. a. How many words (including nonsense words) can be written using all the letters of "happy holidays"? (Come to think of it, I am pretty sure most of them are nonsense!) b. Suppose you have 4 yellow tiles, 6 blue tiles, 5 white tiles and a green tile. If the tiles are lined up in a row, how many c. How many arrangements are there of the tiles if all the blue tiles are together? d. EXTRA CREDIT How many arrangements of the tiles are there if no blue tiles are together? FOUR.. a. Write out the first seven rows of Pascal's Triangle and use your work to find

Explanation / Answer

3.a

Using permutations:

HAPPY HOLIDAYS

Total alphabets = 13

there are,

two H's

two P's

two A's

two Y's

So total possible words will be = 13!/(2!*2!*2!*2!)

= OR 389188800

b)

total tiles = 4+6+5+1 = 16

yellow = 4, blue=6; white=5;green =1

Total arrangements = 15!/(4!*6!*5!) [divide because they are repeating]

c)

If all blue tiles are together ,we can consider them as 1 tile .

so now total tiles will be = 4+1+5+1 = 10

Arrangements = 10!/[4!5!]

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