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Printimc
counting and probability intermediate
Problem
All of David's telephone numbers have the form , where , , , , , , and are distinct digits and in increasing order, and none is either or . How many different telephone numbers can David have?
(A)
(B)
(C)
(D)
Solution
The only digits available to use in the phone number are , , , , , , , and . There are only spots left among the numbers, so we need to find the number of ways to choose numbers from . The answer is then Alternatively, we could just choose out of the numbers not to be used. There are obviously ways to do so. Note: for each combination of 7 numbers, exactly 1 is in increasing order
Final answer
D