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Sagot :
Using the probability concept, it is found that there is a [tex]\frac{1}{420}[/tex] probability that Ernie can create a palindrome using all five tiles.
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- A probability is the number of desired outcomes divided by the number of total outcomes.
- A palindrome word is a word that is read the same on both directions, for example, ANBNA.
- The order in which the letters are chosen is important, thus, the permutation formula is used to find the number of total outcomes.
- These following palindrome words are possible choosing 5 tiles from the word BANANAS: ANBNA, NABAN, ANSNA, NASAN, ANANA, NAAAN, that is, 6 palindrome words.
Permutation formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
- The number of total outcomes is a permutation of 5 elements from a set of 7, thus:
[tex]T = P_{7,5} = \frac{7!}{(7-5)!} = \frac{7!}{2!} = 2520[/tex]
The probability is:
[tex]p = \frac{6}{2520} = \frac{1}{420}[/tex]
[tex]\frac{1}{420}[/tex] probability that Ernie can create a palindrome using all five tiles.
A similar problem is given at https://brainly.com/question/21586984
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