How many 7 digit telephone numbers can be formed if the first digit cannot be 0 or 1
Question 115912: How many 7-digit telephone numbers are possible if the first digit cannot be 0 and (a) only odd digits may be used? (b) the telephone number must be a multiple of 10 (that is, it must end in 0) (c) the telephone number must be a multiple of 100? (d) the first 3 digits are 481 (e) no repetitions are allowed? Answer by checkley71(8403)  You can put this solution on YOUR website! Show
Video TranscriptIn this problem we have been asked how many different 7 dis telephone numbers can be formed. If the first is, it cannot be 0, so we have a 7 dis telephone number. So 1234567 point now note that this first digit cannot be 0, so it will be any 1 of the 9 digits from 1 to 9, which means that there are 9 options to choose from when selecting this first digit. Now we don't have any restrictions on the remaining digits, so for the second digit it can be any 1 of the 10 digits from 0 to 9. So there are 10 options to choose from when selecting the second digit. Similarly, there are 10 options to choose from for the third digit 10 options to choose from for the fourth digit and 10 options for the remaining digits, as well now using the multiplication rule of counting. If we multiply these numbers, then we will have the number of ways of selecting each of these 7 digits and that will give us the number of different 7 digits telephone numbers possible. So we multiply these numbers and we end up with 9000000. That is, we have 9000000 in so the total number of different seventies of telephone numbers that will be 9000000. (b) 7970000 For the first digit there are 8 choices (out of 10 digits) as 0 and 1 cannot be used. Since repetition can be done, the 2nd digit and the 3rd digit have 10 choices each. So, the first three digits can be filled in (8 × 10 × 10 – 3) ways (We need to exclude the numbers 555, 411 and 936 also from first three digits) The last four digits of the telephone number can be filled in (10 × 10 × 10 × 10) ways. ∴ Total number of seven digit phone numbers = (8 × 10 × 10 – 3) × 10 × 10 × 10 × 10 = 7970000. number of 7 digit numbers ( including leading 0): 10,000,000 number of 7 digit numbers including lead 0 or 1 : - 2,000,000 number of 7 digit numbers not lead by 0 or 1 : 8,000,000 This more just taking a complement of a set. ( so an interior form of inclusion-exclusion) You could realize all 7 have at least 8, get $8^7$ then realize each of 6 have 2 more with the seventh having $8=2^3$, for $2^9$ and have fun adding up all $64=2^6$ combinations all together. More a property of a powerset which relates to combinations, as the total number of combinations of all sizes, is the number of distinguishable states which in includes all subsets, (Also tedious) Probability Permutations Brianna F. Follow • 1 Add
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AKSHAY M. answered • 04/30/20 Tutor 5 (1) Masters in Quantitative Finance See tutors like this See tutors like this Possibilities for the 1st digit - 8 (all except 0 or 1) Possibilities for all other digits - 10 ( all numbers from 0-9) So in total we have - 8 * 10^6 possibilities. Upvote • 0 Downvote Add comment More Report Still looking for help? Get the right answer, fast.Ask a question for free Get a free answer to a quick problem. ORFind an Online Tutor Now Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. How many 7 digit phone numbers are possible if the first digit Cannot be 0 and 1?Therefore, we have 544320 ways of seven-digit phone numbers can be formed if the first digit cannot be 0 and repetition of digits is not permitted.
How many seven= 8,000,000. Therefore, according to the condition that the first digit cannot be either 1 or 0, we can have 8,000,000 possible ways of creating a seven-digit area code. Now, according to the other condition which states that the first three-digits cannot have the numbers 911 or 411.
How many 4 digit numbers can be made using 0 7 with none of the digits being repeated?Hence, there are 4⋅7⋅6⋅5=840 possible numbers in this case.
How many combinations of 7 digits are there?Hence, answer is 90,00,000.
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