## A company plans to assign identification numbers to its employees. Each number is to consist of four different digits

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### A company plans to assign identification numbers to its employees. Each number is to consist of four different digits

by BTGmoderatorDC » Sat Feb 26, 2022 6:29 pm

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A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

OA B

Source: GMAT Prep

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### Re: A company plans to assign identification numbers to its employees. Each number is to consist of four different digit

by swerve » Sun Feb 27, 2022 6:50 am
BTGmoderatorDC wrote:
Sat Feb 26, 2022 6:29 pm
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000

OA B

Source: GMAT Prep
Since we have to form $$4$$ digit number with the 1st digit non-zero and all different digits.
It can be formed in the following way

$$1$$st digit$$\Rightarrow \, 9$$ ways $$(1 to 9)$$
$$2$$nd digit $$\Rightarrow\, 9$$ ways $$(0$$ to $$9$$ excluding $$1$$st digit$$)$$
$$3$$rd digit $$\Rightarrow \, 8$$ ways $$( 0$$ to $$9$$ excluding $$1$$st and $$2$$nd digit$$)$$
$$4$$th digit $$\Rightarrow\, 7$$ ways $$(0$$ to $$9$$ excluding $$1$$st, $$2$$nd and $$3$$rd digit$$)$$

So total no. of ways $$= 9\cdot 9 \cdot 8 \cdot 7 = 4536$$ ways

Hope this helps!

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