Which of the following are partitions of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}? O {2, 4, 6, 8}, {1, 3, 5, 9}, {7, 10} O {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} O {1, 2, 4, 8}, {2, 5, 7, 10}, {3, 6, 9} O {3, 8, 10}, {1, 2, 5, 9), (4, 7, 8}

Q: c. How many ways can you choose 3 pieces from the 4 kings and queens (black king, white king, black…

A: Here, order matters. Therefore permutation rule can be applied. Permutation Rule: A permutation is…

Q: How many possible ways are there to arrange the six items into the four boxes in such a manner that…

A:

Q: In how many ways can four elements be selected from A such that their sum is less than 45?

A: The data set is given as follows:

Q: How many distinct 5 block partitions can be made of the set A={1, 2, 3, 4, 5, 6} ?

A: Given set is          To find the number of distinct 5 block partitions that can made…

Q: Select the collection of sets that forms a partition of: {1, 2, 3, 4, 5, 6, 7, 8} {0,1,2,5,7}…

A:

Q: Find the number of stack permutations of {1, 2, 3, 4, 5}.

A: We have to find the number of stack permutations of

Q: How many unordered sets are there of six items chosen from eight? ?sets

A: The different groups that can be formed by choosing r  things from a given set of n different thing…

Q: same

A:

Q: How

A:

Q: A standard deck of cards has 52 cards. There are four suits: ♥, ♦, ♣, ♠. For each suit, there are…

A: Conditions:• The first group has three cards of the same denomination.• The second group has three…

Q: If A=(1,2,3,4,5.6,7), What is the number of nonempty subsets of A?

A:

Q: True or False {2,3} is a subset of {-1,2,5,6}

A: Here {3} is not an element of the given set.

Q: Bill and Kim Johnson are purchasing a house for $336,000. Their bank requires them to pay a 10% down…

A: To calculate the total amount, we need the following information:

Q: How many permutations of {1,2,3,4,5,6,7} have exactly one element fixed?

A: Using inclusion-exclusion principle to compute the given permutation: There are 71·6! ways to select…

Q: Find the number of permutations of 4 distinct objects. There are permutations.

A: Permutation: Permutation is an arrangement  of items in a permanent order. In permutations  Orders…

Q: Let S={1,2,3,4,5,6,7,8,9,10,11}   How many subsets contain at least one odd number?

A:

Q: I have a bucket of n green balls labeled 1, 2, . . . , n. I have another bucket of red balls labeled…

A: The events are occurring simultaneously. So,  Total combinations=combinations for green…

Q: If B = {3, 7, 10, 12} How many subsets of B can be formed?

A: 24 subsets of B can be formed.   The detailed solution is as follows below:

Q: A multiset is a collection of objects, just like a set, but can contain an object more than once…

A:

Q: Is A a subset of B if A = {2, 3, 5, 7, 8, 9, 10} andB = {3, 5, 8, 9}?

A: The given sets are, A=2,3,5,7,8,9,10B=3,5,8,9 A set A can be said to be the subset of another set B…

Q: How many ways can you choose 3 pieces from the 4 kings and queens(black king, white king, black…

A:

Q: onsider the 4-lists taken from {1,2,3}. For example, (1,2,1,3).  How many are there in which each…

A:

Q: A deck of 52 cards is equally dealt to 4 players. Find the number of ways to distribute the cards so…

A: 52 cards are equally dealt by 4 players. So, each player will get 13 cards. To determine the…

Q: 2. Show that the combination of choosing r items from a set of n items has the same possible…

A: Combination can be defined as the number of ways of merging things disregarding of their orders.  It…

Q: How many unordered sets are there of two items chosen from four? ?sets

A: We have to find number of unordered sets of two items chosen from four items.

Q: If 8 subjects  are selected from the 12 that are available  and the 8 selected subjects are all…

A: Given that 8 subjects are selected from the 12 subjects. The selected 8 subjects are all treated at…

Q: In how many ways can 7 black and 7 white balls be distributed into 7 boxes so that there are exactly…

A: Given : 7 black and 7 white balls 7 B , 7 W Given boxes = 7  there are exactly 2 balls in each box…

Q: How many subsets are there of the set N = {1, 44, 65, 11, 39, 53, 26}?

A: Given,          The set is N=1, 44, 65, 11, 39, 53, 26We know that,          The number of subsets…

Q: How many ways can one select a subset of 10 elements from {1, 2, 3, . . . , 1000} so that the…

A: We use the following summation: Crn+Cr-1=Crn+1nCmm+Cmm+!+Cmm+2+...+Cmn=…

Q: In how many ways can a selection of 3 men and 2 women can be made from a group of 5 men and 5 women…

A: First find in how many ways can women and men be chosen.

Q: In 1992, the moose population in a park was measured to be 3790. By 1999, the population was…

A: In 1992, the population in park is 3790  In 1999 the population in 3440 Time t1 since 1990 is 2…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.