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Ex 7.1, 4 - How many 5–digit telephone numbers can be constructed - Fundamental principal of counting

 

  1. Class 11
  2. Important Question for exams Class 11
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Ex 7.1, 4 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? The telephone number is of 5 digits and first 2 numbers are 6 and 7 Hence number is of the form Digits between 0 to 9 = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Total number of digit between 0 to 9 = 10 1st & 2nd place is fix 3rd place – After fixing 67 only 8ways to (10 – 2) fill 3rd place . 4th place – After fixing 6, 7, & 3rd place & 4th place, only 7ways (10 – 3) 5th place – After fixing 6, 7, 3rd place & 4th place, only 6 ways (10 – 4) to fill 5th place No. of telephone number that can be formed = 8 × 7 × 6 = 336

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