(a) How many different collections of 50 coins can be chosen if there are at least 50 of each kind of coin? 23426 collections (b) If the pile contains only 25 quarters but at least 50 of each other kind of coin, how many collections of 50 coins can be chosen? 20150 x collections (c) If the pile contains only 40 dimes but at least 50 of each other kind of coin, how many collections of 50 coins can be chosen? 23140 X collections (d) If the pile contains only 25 quarters and only 40 dimes but at least 50 of each other kind of coin, how many collections of 50 coins can be chosen? 19864 X collections

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

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Q: How many different seven-digit telephone numbers can be formed if the first digit cannot be zero?

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Q: How many 5 digit even numbers can you form using all of the digits 1, 2, 3, 3, 5?

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Q: How many three-digit number with no repeat can we make using digits from {1,2,3,4,5}

A: three-digit number with no repeat can we make using digits from {1,2,3,4,5} here we have 5 choices…

Q: How many 5-digit numbers can be created such that no digit is repeated?

A: We need to create 5 digit number  Total digit = 10 ( 0 - 9) 0 cannot be the first digit  1st digit =…

Q: How many different 3-digit numbers are possible using only the digits 2,3,5,6 ?

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Q: From the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, if five-digit numbers are to be formed and…

A: As per our guidelines we are supposed to answer only 3 sub-parts of any one question We have given…

Q: How many different three-digit numbers can be formed using the digits 1, 5, 9, 7, 4, 8, and 6…

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Q: d 3?

A: for a 4 digit even number

Q: How many different three-number “combinations” are possible on a combination lock having 46 numbers…

A: Given,A lock having 46 numbers on its dial.

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

Q: How many four-digit even numbers are possible if the leftmost digit cannot be zero? Repetition is…

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

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.