Uma rede de supermercados fornece a seus clientes um cartão de crédito cuja identificação é formada por 3 letras distintas (dentre 26), seguidas de 4 algarismos distintos. Uma determinada cidade receberá os cartões que tem L como terceira letra, o último algarismo é zero e o penúltimo é 1. A quantidade total de cartões distintos oferecidos por tal rede de supermercados para essa cidade é A) 33600 B) 37800 C) 43200 D) 58500 E) 67600

The correct option is (A) 33,600.

Step-by-step explanation:

The question is:

A supermarket chain provides its customers with a credit card whose identification is formed by 3 different letters (among 26), followed by 4 different digits. A given city will receive cards with L as the third letter, the last number is zero and the penultimate is 1. The total number of distinct cards offered by such supermarket chain for that city is A) 33600 B) 37800 C) 43200 D) 58500 E) 67600

Solution:

The general format of the credit cards provided by a supermarket chain is as follows:

X X X # # # #

Here, X represents letters and # represents numbers.

All the three letters have to different and all the four numbers have to different, i. e. no repetition allowed.

It is provided that a given city will receive cards with L as the third letter, the last number is zero and the penultimate is 1.

Then the general format of this cities credit cards is as follows:

X X L # # 1 0

Now there are two spaces left for letters and 2 for numbers.

As there are no repetition allowed the two letter spaces can be filled by:

Number of ways to select 2 letters = 25 * 24 = 600

And the number of ways to select two numbers when there is no repetition allowed is:

Number of ways to select 2 numbers = 8 * 7 = 56

Compute the total number credit cards available at the supermarket as follows:

Total number credit cards = 600 * 56 = 33600

Thus, the total number of distinct cards offered by such supermarket chain for that city is 33,600.

The correct option is (A).