Question

Code is formed using four of these letters: A, B, I. K, N, O, and T. (Note that the order of the letters in the code matters; for example, ABIK

different code from BAIK.
The size of the sample space is
. The probability that the first three letters of the four-letter code are vowels is

Answer 1

The size of the sample is 840.

The probability that the first three letters of the four-letter code are vowels is=\frac{1}{35}=

35

1

Explanation:

Th total number of letters given to form code of 4 letters = 7

Since, the order of the letters in the code matters, which means there is no repetition.

The total number of ways to form the code size =7*6*5*4=8407∗6∗5∗4=840

Therefore, The size of the sample is 840.

Since, there are 3 vowels and rest of 4 letters are consonant.

The number of ways to form code such that the first three letters of the four-letter code are vowels =3\times2\times1\times4=243×2×1×4=24

The probability that the first three letters of the four-letter code are vowels is

=\frac{24}{840}=\frac{1}{35}

840

24

=

35

1