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  4. How many 5-digit telephone number can be constructed using the digits 0 to 9 , if each number starts with 67 and no digits appears more than once?

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Q. How many 5-digit telephone number can be constructed using the digits 0 to 9 , if each number starts with 67 and no digits appears more than once?

MHT CETMHT CET 2021

Solution:

Since, telephone number start with 67 , so two digits is already fixed. Now, we have to do arrangement of three digits from remaining eight digits.
$\therefore$ Possible number of ways $={ }^8 P_3$
$=\frac{8 !}{(8-3) !}=\frac{8 !}{5 !}=8 \times 7 \times 6=336 \text { ways }$