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irinina [24]
3 years ago
13

Five digit serial numbers for a product are to be made using letters and/or numbers, e.G. JGR29. The serial number could have al

l letters, all numbers or a mix of both. Repetition of characters is NOT allowed. How many such serial numbers can be made?
Mathematics
1 answer:
S_A_V [24]3 years ago
5 0

Answer:

1,404,000 serial numbers can be made

Step-by-step explanation:

For the five digit serial numbers, since all letters and all numbers could be used, then we can use 26 letters (A,B,C,...Z) and 10 numbers (0,1,2,...9).

Now, say the letters and numbers are to occupy the labeled spaces below

_  _  _  _  _

1   2  3  4  5

(NOTE: Spaces 1,2,3 are to be occupied by any of the 26 letter while spaces 4 and 5 are to be occupied by any of the 10 numbers)

For space 1, there are 26 possibilities

For space 2, there will be (26 -1 ) 25 possibilities (since repetition of characters is NOT allowed)

For space 3, there will be (26-2) 24 possibilities (since repetition of characters is NOT allowed)

For space 4, we have 10 possibilities

and for space 5, we (10-1) 9 possibilities (since repetition of characters is NOT allowed)

Therefore, the number of serial numbers that can be made is

26 × 25 × 24 × 10 × 9 = 1404000

Hence, 1,404,000 serial numbers can be made

OR

Using permutation, nPr = n!/(n-r)!

For the letters,

n is the total number; n = 26

and r is the number of available spaces, r = 3

For the numbers,

n = 10

r = 2

Then, we get

26P3 × 10P2

26!/(26-3)! × 10!/(10-2)!

26!/23! × 10!/8!

15600 × 90 = 1404000

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There is only one solution for the equation 4z + 2(z -4) = 3z + 11 because the exponent for the power of z is 1.

<h3>What is an equation?</h3>

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

<h3>What is the Solution?</h3>

A solution is any value of a variable that makes the specified equation true.

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