Permutations

Question

In how many ways can four letters from COFFEE be picked considering all permutations?

Comments

$6! / 2! * 2!$

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i think answer should be 102

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We have to pick "4 letters" from "COFFEE" - can someone explain the remaining part of the question?

Answer 1

ANSWER - 360 ways

To pick four letters from the word "COFFEE", we can use permutations directly since the order matters.

The word "COFFEE" has 6 letters, and you want to pick 4 of them. So, we have:

\[ P(6, 4) = \frac{{6!}}{{(6-4)!}} = \frac{{6!}}{{2!}} = 6 \times 5 \times 4 \times 3 = 360 \]

So, there are 360 ways to pick four letters from "COFFEE" considering all permutations.

Comments

shouldn't u've to divide this again with 2! ? coz there are 2 letters which are same here isn't it ?

Answer 2

In the word "COFFEE", 

C - 1, O - 1 , E - 2, F - 2.

Distinct Letters are C, O, F, E.

Case 1 : All four letters to selected is different.

The Number of Ways = ⁴C₄ = 1

Case 2 : When out of four letters to selected 2 E is Present.

The Number of Ways = ³C₂ = 3

Case 3 : When out of four letters to selected 2 F is Present.

The Number of Ways = ³C₂ = 3

Case 4 : When 2 E and 2 F is Present.

The Number of Ways = 1

 

Total ways of selecting 4 Letters will be = 1 + 3 + 3 + 1 = 8