number-problem---4-digit-password - GCSE Solutions - Central collection of solutions to all the Mathematics GCSE problems in the book, exams and past papers

5 Number problem- 4 digit password

Exam Style question:

Jess has a 4-digit password for her mobile phone. Each digit can be between 0 and 9 inclusive.

a) How many choices are possible for each digit of the code?

b) What is the total number of 4-digit passwords that Jess can create?

Jess would like to choose an even number. The code can start with zero.

c) How many different ways are possible now?

Solution:

a) 0-9 digits has 10 different possibilities.

b) There are 4 digits : 10 x 10 x 10 x10 = 10,000.

c) Even= 0, 2, 4, 6, 8 ; Odd : 1, 3, 5, 7, 9

There are 5 even and 5 odd.

Even = $\frac{5}{10} = \frac{1}{2}$ of the numbers are even.

So, $\frac{10, 000}{2} = 5000$ .

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Ruhi Quadri Published on 05 Nov 2020