Serial numbers for an item produced in a factory are to be made using two letters followed by four digits (0 to 9). If the letters are to be taken from six letters of English alphabet without repetition and the digits are also not repeated in a serial number, how many serial numbers are possible?

In the question, we have to find the possible number of 4 digits and 2 alphabetical place serial numbers formed by the numbers 0 to 9 and with only 6 English alphabets when repetition of digits and alphabets is not allowed.

We will use the concept of multiplication because there are six sub jobs dependent on each other because a number and alphabet appearing on any one place will not appear in any other place.

In first position from left we have 6 alphabet choices, so in the second position, we will have 5 choices because no repetition is allowed. On the first position from left for digits or third position from the left of serial number we will have 10 choices, and for next position, we will have 9 choices, the number of choices will decrease by one as we keep on going right side. Because on serial numbers we can write zero on the left most position of numbers.

The number of ways in which we can form four digit with two alphabets serial numbers with the help of given data is 6 × 5 × 10 × 9 × 8 × 7 = 151200

Note the positions of the two alphabets is fixed that is the first two and then four digits are placed afterward if the positions were not fixed then the answer would vary.

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