A teacher has 24 colored pencils and 18 pictures to be placed in groups with the same number of pencils in each group and the same number of pictures in each group. If each group must have the same type of items, how many groups of pencils and how many groups of pictures can be made? How many of each item will be in

Q: Suppose Pat has eight shirts and four pairs of pants. How many different outfits  can Pat make by…

A: The person has 8 shirts and 4 pairs of pants and he can make one outfit by combining one shirt with…

Q: How many different license plates can be made if each is to display 3 numbers and 3 letters?

A: We have to find out no. Of ways...

Q: Mark packed 8 shirts, 3 pairs of pants and 2 pairs of shoes for their trip. How many outfits can he…

A:

Q: john has 10 apples and kate took 5 away how many apples are left?

A: When kate take you are subtracting.   John  originally had 10

Q: How many dozen doughnuts must be ordered for a meeting if 156 people are expected to attend, and…

A: To determine how many dozen doughnuts must be ordered for a meeting if156 people are expected to…

Q: If Tim has 6 apples in each bag and he has 12 bags each, how many apples does he have all together?

A: Use unitary method.

Q: if  there was 56 students and 8 groups how many were in each group

A: Given that  Number of students=56 Number of groups=8 To find Number of students in each group.

Q: Ten children are to be divided into an A team and a B team of 5 each. A team will play in one league…

A: Given Information:   The total number of children, n=10 The number of children divided into the two…

Q: A man owns 8 pairs of pants, 15 shirts, 12 ties, and 3 jackets. How many different outfits can he…

A: Given he has 8 pairs of pants, 15 shirts, 12 ties, and 3 jackets

Q: A company charges $20 to make one monogrammed shirt, but reduces this cost by $0.10 per shirt for…

A: Given,Charges for first shirt = $20.Reduces cost per shirt for additional shirt upto 100 shirst =…

Q: In a group of dogs and their owners, there are exactly 20 heads and 64 legs.  How many dogs are in…

A: Let, x be No of men. y be no of dogs   Men consists of 2 legs and dog has 4 legs.   x+y=20 2x+4y=64

Q: In a class, there are 12 kids. If six kids are wearing socks, 4 wearing shoes O points and 3 are…

A:

Q: Lina has a China figurine, a glass figurine, and a soapstone bear. In how many ways can she choose…

A: Lina has a China figurine, a glass figurine, and a soapstone bear.

Q: Sally has 2 pairs of shoes, 9 pairs of pants, and 8 shirts. How many different outfits can she make…

A: Sally can make, 2×9×8 = 144 different outfits.    The detailed solution is as follows below:

Q: A customer needs 60 pencils. If he buys them on sale, how many of the 60 pencils can he get for…

A:

Q: ario painted identification letters on his bicycles so that he could track which ones are being used…

A: Since every cycle is coded with three letters of English alphabets, which starts with alphabet M.…

Q: Jana has 10 blouses, 5 pairs of shoes, 5 skirts,and 5 hats. How many distinct 'outfits' does she…

A: No.of blouses=10 no.of pairs of shoes=5 no.of skirts=5 no.of hats=5

Q: Agustina owns all five books in the Spiderwick Chronicles series. In how many different orders can…

A: Given: Number of books = 5

Q: The newest cars have 12 different accessories and the buyer pays for each one separately.  If a…

A: Given, The newest cars have 12 different accessories A buyer wants to buy four accessories

Q: Jose has 52 coins among which there are only nickels and pennies. If the value of the coins is…

A: We can use simultaneous equations in order to solve the given problem.

Q: If someone owns: 7 pants 1 shirt 5 ties 7 jackets, how many different outfits can that person make?

A: We have given that someone owns: 7 pants 1 shirt 5 ties 7 jackets

Q: Twenty children are to be divided into an X team and a Y team of 10 each. The X team will play in…

A:

Q: A basketball team contains 20 players. If 5 people can be on the court at one time, how many…

A: Total number of players is 20. The number of player to be court at one time is 5.

Q: John has five shirts, three pants, two jackets, and three pairs of shoes. How many different outfits…

A:

Q: ill has 11 shirts and 6 pairs of pants. Assuming that everything matches, how many different outfits…

A: Answer - Jill has 11 shirts and 6 pairs of pants. Assuming that everything matches,…

Q: Leah and Andi are purchasing photo albums of their wedding pictures as a thank you to their parents.…

A: Given, No of album sizes=3 No of cover options=5 No of different pages= 2 unique photo album…

Q: Each day, Mr. Ling has a boy and a girl summarize the assignment for the day. There are 7 boys and 8…

A:

Q: If there are 9 apples and my sister ate 3, how many apples are left?

A:

Q: During a summer camp, all the children have to be separated into 8 different groups. If there were…

A: During a summer camp, all the children have to be separated into 8 different groups. If there were…

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.