Consider the set {1,2,3}. i. Write the elements of the permutations by taking two digits from above three ii. Write the elements of the permutation without repetition of the 3 numbers taken all 3 at a time. iii. Do both cases (i) and (ii) have the same number of elements?

List all the ways to select two members from S with repetition. The order in which the members are selected is not important. For example, DD is allowed and BA is the same selection as AB. S= {H, J, K, L, M} ....D Identify the list of all the ways to select two members from S, allowing for repetition. Choose the correct answer below. O A. HH, HJ, HK, HL, HM, JJ, JK, JL, JM, KK, KL, KM, LL, LM, MM O B. HH, HJ, HK, HL, HM, JK, JL, JM, KL, KM, LM OC. HH, HJ, HK, HL, HM, JH, JJ, JK, JL, JM, KH, KJ, KK, KL, KM, LH, LJ, LK, LL, LM O D. HK, HL, HM, JK, JL, JM, KL, KM

3: At a Chinese restaurant, dinner for 8 people consists of 3 items from column A, 4 items from column B and 3 items from column C. If columns A, B and C have 5, 7 and 6 items respectively how many different dinner combinations are possible?

A group of 8 people, including Betty and Bob, are going to take a group photo. In how many ways can they line up, order counting, if Betty and Bob must stand next to each other?    ___________

d. [Permutation] Solve the following problems - Find the number of words that can be formed by using the letters of the word "DEMOCRACY" where first letter will be always C and last letter will be R. e. [Combination] A group of 15 students is to be formed from 44 students of MATI00 Course. Among the students of the course there is 2 renowned batsmen, 3 spinners, 2 fast blowlers and 2 wicketkeepers. How many different ways this can be done so as always to (i) include 1 renowned batsman, 1 fast bowler, 1 spinner and 1 wicketkeeper; and (ii) exclude spinners? 2.

Subparts 2-4

2. I found some bingo cards in our classroom. A bingo card seems to have 5 rows and 5 columns. The center cell is blank, but the remaining cells each contain a number. No two cells contain the same number. In the first column, integers from 1 to 15 are used. In the 2nd column, integers from 16 to 30 are used, and so on. Thus, in the 5th column, integers from 61 to 75 are used. How many different bingo cards are there? Explain.

A jeweler has 10 diamonds and 7 rubies. To make a bracelet, a jeweler will select 5 gemstones. Blank #1: Is this a Permutation or Combination? Blank #2: How many selections will contain at least 3 diamonds? Blank # 1 combination Blank # 2 8:14 PM 4/24/2021 Delete が+ F12 PrtSc Insert F10 F11 Backspace Num Lock 0 7 8. Home PgUp 4 %3D 7. Enter 2 Shift End Pg PgUp + II

How did they get the numbers in venn diagram break down step by step