The probability the letters will spell the word ENVELOPE is 1/6720 option (D) 1/6720 is correct.
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
If all the letters in the word ENVELOPE are randomly rearranged,
As we know, a permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
From the definition of the permutation and combination we can calculate the total number of arrangements:
E :: 3
N :: 1
V :: 1
L :: 1
O :: 1
P :: 1
The arrangement Letters:
E,L,N,O,P,V
Total Number of Letters:
8
Total Number of Unique Letters:
6
Total arrangements = 8!/3!
Total arrangements = 8×7×6×5×4
Arrangements = 6720
Total number of outcomes = 6720
Number of favorable outcomes = 1
Probability = 1/6720
Thus, the probability the letters will spell the word ENVELOPE is 1/6720 option (D) 1/6720 is correct.
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