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PERMUTATIONS AND COMBINATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPERMUTATIONS AND COMBINATIONS2 Marks
Question
How many 5-digit telephone numbers can be constructed using the digits 0 to 9, if each number starts with 67 and no digit appears more than once?
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Answer

According to the problem, 2-digits i.e. 6 and 7 are fixed. Thus, 10 - 2 = 8-digits can be used in constructing the telephone numbers. There are 8-digits 0, 1, 2, 3, 4, 5, 8, 9.
The first number can be selected in 8 ways. After the selection of the first digit, we have 8 - 1 = 7-digits in hand, second digit can be selected in 7 ways and the third digit can be selected in 6 ways.
According to the fundamental principle of multiplication (FPM), the number of ways of selecting a digit for remaining three places:
= 8 $\times$ 7 $\times$ 6 = 336 ways

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