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Komok [63]
3 years ago
12

how many different license plates are possible if each contains 2 letters(out of the alphabet’s 26 letters) followed by 5 digits

(from 0 to 9)? how many of these license plates contain no repeated letters and no repeated digits?
Mathematics
1 answer:
timofeeve [1]3 years ago
3 0

Answer:

total number of license plates : 676000

total number of license plates with no repeated letters and no repeated digits : 468000

Step-by-step explanation:

i) the license plate is to be made up of two letters (out of 26 alphabets) followed by 5 digits ( from 0 to 9).

therefore the total number of combinations for license plates when repetitions of digits and numbers are allowed will be given

26 × 26 × 10 × 10 × 10 = 676000

ii) the number of license plates containing no repeated letters and no repeated digits will be given by

26 × 25 × 10 × 9 × 8 = 468000

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english has 26 different letters. how many consecutive words have to be selected in a book to have at least 5 that start with th
Valentin [98]

The words need not be English language words  142506

What is permutation and combination?

A set of elements can be divided into subsets in two different ways: combination and permutation.

                          The components of the subset may be arranged in any order when combined. The components of the subset are listed in a permutation in a certain order.

If the word has 5 different letters  then it is just 26-choose-5 or (26/5).

If the word has 4 different letters  then it is just 26-choose-4 or (26/4)

have 4 options to choose which letter to duplicate twice.

This gives =  4*(26/4)

If the word has 3 different letters  then it is just 26-choose-3 or (26/3).

you duplicate one of the three letters 3 times - 3 options for that, or you choose 2 letters and duplicate each one twice - again 3 options. In total this gives  = 6*(26/3).

If the word has 2 different letters  then it is just 26-choose-2 or (26/2).

The sets of 2 different letters and duplicate either one of the letters 4 times - 2 options; or duplicate one letter 2 times, and the other 3 times - again 2 options. In total this is  = 4*(26/2).

The word has just 1 distinct letter you have =  (26/1).

we get :

N = (26/5)+ 4*(26/4) + 6*(26/3) + 4*(26/2) +  (26/1)

= 142506

The words need not be English language words  = 142506

Learn more about  permutation and combination

brainly.com/question/28065038

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5 0
1 year ago
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Nataly_w [17]

Answer: 0.939\ or\ 93.9\%

Step-by-step explanation:

Given

Survey shows that 16% of college students have dogs and 38% have HBO subscription

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\Rightarrow P_o=0.16\times 0.38\quad [\text{As both events are independent}]\\\Rightarrow P_o=0.0608

The probability that the random person has neither of the two is

\Rightarrow P=1-P_o\\\Rightarrow P=1-0.0608\\\Rightarrow P=0.939

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