How many different four letter words can be formed (the words need not be meaningful) using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?
hard this one, could you explain step by step please?
Permutation Combination of words
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- asamaverick
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Consider the four letter as
E _ _ R
We are asked to fill the remaining two letters. Since E & R has already been picked form MEDITERRANEAN what remains is
M D I T R EE AA NN
So we have to pick 2 letters out of 11. But the important thing here is that E , A & N are repeated.
So we have 8 unique letters and 3 repeated letters in the remaining 11. The 2 numbers can be selected in the following 2 ways:
1) Both are different : first letter can be selected out of 8 & second one from remaining 7. = 8*7 = 56 ways.
2) Both letters are same: There are on three combinations AA, EE & NN = 3 ways
So total numbers of possibilities = 56 + 3 = 59
What's the OA?
E _ _ R
We are asked to fill the remaining two letters. Since E & R has already been picked form MEDITERRANEAN what remains is
M D I T R EE AA NN
So we have to pick 2 letters out of 11. But the important thing here is that E , A & N are repeated.
So we have 8 unique letters and 3 repeated letters in the remaining 11. The 2 numbers can be selected in the following 2 ways:
1) Both are different : first letter can be selected out of 8 & second one from remaining 7. = 8*7 = 56 ways.
2) Both letters are same: There are on three combinations AA, EE & NN = 3 ways
So total numbers of possibilities = 56 + 3 = 59
What's the OA?
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The word starts with E and ends with N
E _ _ N
We have 8 unique letters in the word. We already have used two[E and N]. So we have 6 letters for remaining two places.
6 x 5 = 30 possibilities.
Is it correct? What is OA?
E _ _ N
We have 8 unique letters in the word. We already have used two[E and N]. So we have 6 letters for remaining two places.
6 x 5 = 30 possibilities.
Is it correct? What is OA?
- amising6
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How many different four letter words can be formed (the words need not be meaningful) using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?
now simple condition E_ _ R
now there are two case
1st case
when repetaion is not allowed E _ _ R
1 2 3 4 (position of blank)
as letter need to be start by E so 1 st position can be filled in 1 way
as there are 13 letter in that word second position can be filled in 6 ways ( there are only 8 distinct letter and E has occupied first place and R occupies last place )
since repeatation not allowed of of letter 3 rd place can be filled in 5 ways (as 2 letter occupie first place)
as word need to end with R 4 th place can be filled in 1 way
so total number of word formed 6*5=30
second case ) repeatation is allowed
when repetaion is allowed E _ _ R
1 2 3 4
as letter need to be start by E so 1 st position can be filled in 1 way
as there are 13 letter in that word second position can be filled in 13 ways
since nothing said about repeatation of letter even 3 rd place can be filled in 13 ways
as word need to end with R 4 th place can be filled in 1 way
so total number of word formed 1*13*13*1 =169
check OA to find out what is asked i guess if not given anythin we go for repeatation
now simple condition E_ _ R
now there are two case
1st case
when repetaion is not allowed E _ _ R
1 2 3 4 (position of blank)
as letter need to be start by E so 1 st position can be filled in 1 way
as there are 13 letter in that word second position can be filled in 6 ways ( there are only 8 distinct letter and E has occupied first place and R occupies last place )
since repeatation not allowed of of letter 3 rd place can be filled in 5 ways (as 2 letter occupie first place)
as word need to end with R 4 th place can be filled in 1 way
so total number of word formed 6*5=30
second case ) repeatation is allowed
when repetaion is allowed E _ _ R
1 2 3 4
as letter need to be start by E so 1 st position can be filled in 1 way
as there are 13 letter in that word second position can be filled in 13 ways
since nothing said about repeatation of letter even 3 rd place can be filled in 13 ways
as word need to end with R 4 th place can be filled in 1 way
so total number of word formed 1*13*13*1 =169
check OA to find out what is asked i guess if not given anythin we go for repeatation
Ideation without execution is delusion
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