9. Consider a number with 8 digits but using only digits 1, 2, 3 and 4. a) How many numbers can we build? b). How many numbers can we build so that each of the digits 1, 2, 3 and 4 appear at least once? c). How many numbers can we build so that the digit 1 appear exactly 3 times and the digit 2 appears exactly twice?

Q: At one point, license plates in a certain state consisted of 2 letters (excluding I, O, Q, and W),…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Q: The seven given numbers are: 5, 6, 3, 4, 1, 2, and 7. A. How many five-digit numbers can be formed…

A: Given seven numbers are5,6,3,4,1,2,7

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Q: How many numbers can be created? b) How many of them are odd numbers? c) How many of them are…

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Q: How many 4 digit numbers can be formed using only the digits 1, 2, 3, 4, 5,  6?

A: From the provided information, The digits are 1, 2, 3, 4, 5, 6 that is number of elements (n) = 6

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

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Q: How many different 4 digit numbers can be formed using only the digits 3, 5, 7 and/or 9, if each…

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Q: In how many ways can the numbers from 7 to 10 be arranged three at a time if the numbers can repeat?

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Q: How many different 7-digit telephone numbers contain three 5s, two 2s and two 1s?

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Q: How many ways to arrange 5 books on the shelf exist if two definite books are not placed together.

A:

Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

A:

Q: How many 4-diğit humbérš čâh bě fórméd from the digits 1, 3, 5, 6, 8, and 9 if no repetition is allo…

A: Given digits 1, 3, 5, 6, 8 and 9 (Total 6 numbers) We want to find number of 4 digit numbers such…

Q: 15. How many different arrangements of ten cars in order are possible in a parking lot that is made…

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Q: How many 7 digit numbers can be formed using the numbers 0-9 if the first and 5th digit can only be…

A:

Q: 4. Let 0 <r <1 and let T be the smooth manifold of R³ defined by the equation: (z² + y² +r²-2²-1)² -…

A: note :As per the instructions we will only solve parts (4), (5), (6) of the question.

Q: From the digits 4,3,6,1,5 and 7. How many 4 digit numbers can be made w/o repetition that are more…

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Q: a) How many plates are possible when letters and numbers can repeat? Set up the expression that can…

A:

Q: Suppose that there is a bag containing 6 marbles. How many ways can you draw 4 marbles from the bag…

A: The bag contains =6 marbles number of marbles drawn=4

Q: c) Suppose there are 10 people ({A, B, C, D, E, F,G, H, I, J}) who need to be photographed for a…

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Q: Ann remembers the last four digits of a seven-digit telephone number but knows only that each of the…

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Q: d 3?

A: for a 4 digit even number

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Q: In an apartment complex with 10 mailboxes, in how many ways can a mail carrier distribute 10 letters…

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Q: How many seven-digit numbers can be made from the digits 1 to 9 if repetition is allowed?

A: Given that  To find the number of ways of 7 digit number can be made from the 1 to 9

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Q: B) In an exam, students must answer 9 questions out of a total of 12 and must include exactly 5 of…

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Q: 20) Show that the sum of two consecutive integers is always odd.

A: Let x be any integer. Then its consecutive integer can be written as x+1.

Q: Compute P9,2. (Enter an exact number.)

A: