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Ex 7.1, 4 - How many 5–digit telephone numbers can be constructed

Ex 7.1,4 - Chapter 7 Class 11 Permutations and Combinations - Part 2
Ex 7.1,4 - Chapter 7 Class 11 Permutations and Combinations - Part 3

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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 1st digit 2nd digit 3rd digit 4th digit 5th digit Total number of digits between 0 to 9 = 10 Now, 1st & 2nd place is fix 3rd place – After fixing 67 only 8 ways to (10 – 2) fill 3rd place . 4th place – After fixing 6, 7, & 3rd place & 4th place, only 7 ways (10 – 3) to fill 4th place 5th place – After fixing 6, 7, 3rd place & 4th place, only 6 ways (10 – 4) to fill 5th place Thus, Number of telephone number that can be formed = 1 × 1 × 8 × 7 × 6 = 336 Thus, Number of telephone number that can be formed = 1 × 1 × 8 × 7 × 6 = 336

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.