Question

How many 7-digit numbers can be formed if the first digit cannot be 0 or 9 and if the last digit is greater than or equal to 7 and less than or equal to 8? repeated digits are allowed?

Answer 1

Answer: 1,600,000

(this is one single number and not 3 different numbers)

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Step-by-step explanation:

Imagine having seven slots labeled A, B, C, D, E, F, G

Slot A can have 8 choices {1,2,3,4,5,6,7,8}

Slot B can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot C can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot D can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot E can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot F can have 10 choices {0,1,2,3,4,5,6,7,8,9}

Slot G can have 2 choices {7,8}

Multiply out those values: 8*10*10*10*10*10*2 = 1,600,000

In words this value is "one million, six hundred thousand" or we can say it as "1.6 million" as a much shorter more compact format.