Question

a password must be 4 characters long and contain only digits and lowercase english letters. The english alphabet contains 5 vowels. Assuming that digits and letters can be repeated how many differnt passwords contain exactly one vowel?

enter the exact numeric number

Answer #1

**Solution:**

Given: a password must be 4 characters long and contain only digits and lowercase english letters.

The english alphabet contains 5 vowels.

There are 10 digits from 0 to 9 and 26 letters from A to Z.

thus we have 26 - 5 = 21 consonants.

We have to find possible number of differnt passwords contain exactly one vowel.

So that menas password must contain exactly 1 vowel

then remaining three characters would be from 10 digits and 21 consonants.

that is from remaining 10+21 = 31 ( digits+consonants)

thus we have 5 ways to chose a vowel and 31 ways to chose a character other than vowel.

Thus:

1 | 5 | 31 | 31 | 31 |

OR | ||||

2 | 31 | 5 | 31 | 31 |

OR | ||||

3 | 31 | 31 | 5 | 31 |

OR | ||||

4 | 31 | 31 | 31 | 5 |

Thus

Total number of ways = 4 X ( 5 X 31 X 31 X 31 )

We multiply by 4 since we have 4 ways of different arrangements of vowels.

Thus

**Total number of ways = 595820**

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