Find the number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, what will be the 50th word?
Answers
Answer:
60
NAAIG
Step-by-step explanation:
Hi,
Required to find the number of words with or without meaning that can
be made using all the letters of the word AGAIN.
In Alphabetical order, the letters of the word AGAIN are A, A, G, I , N.
There are 4 distinct letters with one letter repeating twice.
Hence total number of words will be 5!/2! = 60.
Words starting with A : 4! = 24
Words Starting with G: 4!/2! = 12
Words starting with I : 4!/2! = 12
Already there are (24 + 12 + 12) so the second next word would be the
50 th word.
Next word starts with NAAGI whose rank is 49
and then comes in the dictionary order is NAAIG whose rank is 50.
Hope, it helps !
Answer:
Step-by-step explanation:
NAAIG
Explanation:
If we were to have a 5-letter word with each letter being different, we could make:
5 ! = 120 words.
However, since there are 2 As, we need to divide by the internal ordering the As can do ( 2!) to eliminate duplicates. So in total we have:
5 ! /2 ! =
120 /2 = 60 words.
Will the 50th word start with N? To see, let's pin the N as the first letter and then see the number of words we can make from the remaining letters:
4 !/ 2 ! =
24 /2 = 12
and so yes, the 50th word will start with N (N starts the words 49 - 60).
The 12 words starting with N are:
NAAGI
NAAIG
NAGAI
NAGIA
NAIAG
NAIGA
NGAAI
NGAIA
NGIAA
NIAAG
NIAGA
NIGAA