A city distributes vehicle identification stickers using a c

A city distributes vehicle identification stickers using a combination of letters followed by a combination of digits, each of which may be used more than once. Determine the number of possible stickers under the given circumstances. Using 4 letters and 2 digits, how many stickers are possible? Using 2 letters and 4 digits, how many stickers are possible? Adding 1 digit before the 4 letters and 2 digits, how many stickers are possible? Using 4 letters and 2 digits, how many stickers are possible?

Solution

A)

The sticker consists of 6 spaces.

Each of the first 4 spaces can be filled by one of 26 alphabets in 26 ways.

the total no of ways in which the four spaces can be filled is 26⁴.

the remaining two spaces can be filled with one of 10 (0-9) ways in 10² ways.

The total no of ways a sticker can be formed is: (26⁴)*(10²)=4569760 STICKERS

B)

Similary the first two spaces can be filled in 26² ways

the rest can be filled in 10⁴ ways

The total no of stickers is (262)(10⁴)=6760000 stickers.

c)

the first space can be filled in one of tten digits in 10 ways.

The sticker consists of 6 spaces.

Each of the next 4 spaces can be filled by one of 26 alphabets in 26 ways.

the total no of ways in which the four spaces can be filled is 26⁴.

the remaining two spaces can be filled with one of 10 (0-9) ways in 10² ways.

The total no of ways a sticker can be formed is: (10)*(26⁴)*(10²)=45697600 STICKERS