2. In how many ways can the 5 Barangay Captains and 6 City Mayors be arranged in a row so that all six city mayors are all together? a. 314,400 b. 518,400 с. 630,000 d. 720,000 _3. How many different permutations can be made from the word "PANDEMYA"? а. 20,160 b. 40,320 c. 60,000 d. 80,640 _4. In how many ways can 7 people be seated at a round table? a. 100 b. 120 с. 720 d. 1200 5. Find the number of ways in which 6 boys, Toni, Chris, Billy, Gil, Nadz and Tabby can be seated at a round table such that Gil and Nadz always sit together. а. 24 b. 48 c. 120 d. 240

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A: We can arrange n things in n! ways in a row.

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A: By using permutation and combination

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A:

Q: any permutations of the letters can be made from the word COCONUT? (Don't Hand writing in solution

A:

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A: Different ways that eight people can sit in a row.

Q: 3. In how many ways can you arrange 5 books on a shelf from available 10?

A: The number of all combination of n things, taken r at  time is given by:

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A: To distribute n things in k places, the formula is n+k-1k-1

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A: Now we have to calculate ,how many 6 letter can be formed if repetition is permitted.

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A:

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A: MISSISSIPPI

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Q: How many different arrangements can b

A: Given the word          "SIPNAYAN"

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.