Counting numbers are to be formed using only the digits 6, 7, and 8. Determine the number of different possibilities for the type of number described below. Four-digit numbers with one pair of adjacent 6s and no other repeated digits (Hint: You may want to split the task of designing such a number into three parts, such as (1) position the pair of 6s, (2) position the 7, and (3) position the 8.) The number of different possibilities for this type of number is. (Type a whole number.)

Q: the set {1,3,4,6,7,8,9}, how many odd numbers can we construct between 100-999 if each element can…

A: We have to solve given problem:

Q: Using the digits 2 through 9, find the number of different 5-digit numbers such that: a. Digits can…

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Q: if these five numbers form a pattern such that the differernce between each pair of numbers is the…

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Q: Use the multiplication principle to solve. A home improvement store website listed 272 different…

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Q: Use the multiplication principle to solve. A home improvement store website listed 278 different…

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Q: How many four digits numbers can be made using 1, 2, 3, 4 and 0? Caution: your numbers cannot start…

A: 9

Q: Jse the multiplication principle to solve. There are different ways to buy the products needed.…

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Q: In a certain state, each automobile license plate number consists of two letters followed by a…

A: There are 24 choices for each letter. (this explanation was already shown in the image you shared)…

Q: 21. Bank checks. Determine the check digits for the following bank codes: 0 25 7 1 1 0 8 .

A: The given code is: 0 2 5 7 1 1 0 8 _

Q: Opposite: Number: 15.5 -15. 5 -20 -18 -16 -14 -12 -10 -8 2 10 12 14 16 18 20 Opposite: Number: -18 4…

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Q: I just need to know why they are all classified that way. An explanation why each number is…

A: We classified the given numbers. Note : As per our Guidelines , we can solve first three subparts .…

Q: How many different two-digit numbers can you form using the digits 3, 8, 7, 4, 1, and 5 without…

A:

Q: In choosing what music to play at a charity fund raising event Cory needs to have an equal number of…

A: If an event can be done in n different ways and an other event can be done in m different ways, then…

Q: Using the digits 2 through 9, find the number of different 6-digit numbers such that: a. Digits can…

A: Answer:- Given digits are -  2,3,4,5,6,7,8,9  Total number of digits= 8

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: At a college, 52 students were members of the choir or the marching band, 25 were members of the…

A: At a college, 52 students were members of the choir or the marching band, 25 were members of the…

Q: How many different ways can the letters of "jogging" be arranged? The number of different ways that…

A: The word “jogging” contains a total of 7 letters in which “g” letter is repeated 3 times.

Q: What can we say about 5"-2" for any natural number n? Justify your response.

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.