A combination lock requires five selections of characters. Each character is either an integer from 0 through 9, an upper-case letter from A through Z, or a lower-case letter from a through z. In other words, there are 62 characters to choose from (10 numbers, 26 upper-case letters, and 26 lower-case letters). Moreover, the locks are constructed in such a way that no character may be used more than once (a) How many different combinations are possible? (b) What is the probability that a randomly chosen combination will have no numbers?

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Q: Fifty (50) students in a school played Basketball and Football. Every student plays at least one of…

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Q: A telephone number consists of 10 digits: 3 digit area code followed by 7 digit number. How many…

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Q: Outside a home, there is an 8-key keypad numbered 1 through 8. The correct five-digit code will open…

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Q: Outside a home, there is a 4-key keypad with letters A, B, C, and D that can be used to open the…

A: Given Outside a home , there is a Keypads with letter= A,B,C,D Number of codes=4

Q: If a men working 6hours a day can do a work in 88days, then 6men working 8hours a day can do it in…

A: Given that men working 6 hours a day can do work in 88 days

Q: The total curb weight of a truck, a car A, and a car B is 11,250 lb. The weight of car A is 15 lb…

A: Given,The total weight of a truck, car A and car B is 11,250 lb. The weight of car A is 15 lb less…

Q: A realtor uses a lockbox to store the keys to a house that is for sale. The access code for the…

A: The total number of digits =10(from 0 to 9) There are 5 digits (1,3,5,7,9) and 5 even digits…

Q: Arealtor uses a lock box to store the keys to a house that is for sale. The access code for the lock…

A: The access code contains 4 digits          Digits : 0,1,2,3,4,5,6,7,8,9 The first digit can…

Q: How many 4-digit numbers are there?   And if repetition of digits is not allowed?

A: Given that n= number from 1 to 9 = 9 r = 4 ( since we have to take 4 digit number)

Q: In 2020, the pandemic caused by COVID-19 has created havoc all around the world. In a small island…

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Q: A census taker visited the Jones household, and asked Mrs. Jones for the age of her three sons. Mrs.…

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Q: Some automobiles have 4 button locks. To gain entry, push each of the four buttons, in a particular…

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Q: Colin has 9 cd’s in his carrying case – two John Tesh, three Michael Jackson, and four Beatles. How…

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A: Introduction: A permutation is a specific arrangement of objects. Set members or elements are…

Q: From the official website of a major league baseball team, it is found that there were seven active…

A: seven active player in a team to play outfield position. there are three outfield positions. no. of…

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Q: In a certain​ country, area codes have six digits and are subject to the following restrictions. The…

A: Given:In a certain country, area codes have six digits and are subject to the following…

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A: Given data: An order for an iPad Pro can specify any one of two sizes (iPad Pro 11‑inch, iPad Pro…

Q: A computer user has downloaded 23 songs using an online file-sharing program and wants to create a…

A: GivenNo.of downloaded songs(n)=23no.of  songs to use in CD player(r)=8

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.