1. A group of 14 must select a president, a vice-president, a treasurer, and a secretary. How many ways can this bedone?2. How many arrangements are there if 8 playing cards are drawn from a deck of 52 cards?3. Find the number of distinct permutations of the letters of the word COMMOTION.4. How many permutations are there of the letters in the word BALLOON if the first and the last letters must eitherbe N or B?5. In how many ways can you seat two children and three adults in a row of five seats if the children are not to sittogether?6. Find in how many ways can two admirals, three generals, and four lieutenants can be seated in a row of nine seatsof (a) the admirals sit at each end. (b) a general sit at each end and the lieutenants in consecutive seats.7. A baseball tgam has 16 players. Suppose that the team has three star players: Ryan, Glenn and Manny, and thatthey must be first, second and third, respectively. How many different batting orders are there for the team?8. Seven boys and seven girls went to watch a movie. How many ways can they be seated if (a) the boys are to sittogether and so with the girls? (b) the boys and the girls are to sit alternately? (c) Grace and Joey are members ofthe group and want to sit together all the time?9. In how many ways can you sit 8 people on a round table (a) if there are no restrictions? (b) if two particular personswant to sit next to each other?10. Crisha has 5 different colored beads including purple and pink. In how many ways can she arrange the beads in astring (a) if there are no restrictions? (b) so that the purple and pink beads are adjacent to each other?

The expression,nCr is evaluated using the formula, nCr=n!(n-r)!r! . The number of ways 1 person can…

Answered: A group of 14 must select a president,…

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A group of 14 must select a president, a vice-president, a treasurer, and a secretary. How many ways can this be done?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

1. A group of 14 must select a president, a vice-president, a treasurer, and a secretary. How many ways can this be
done?
2. How many arrangements are there if 8 playing cards are drawn from a deck of 52 cards?
3. Find the number of distinct permutations of the letters of the word COMMOTION.
4. How many permutations are there of the letters in the word BALLOON if the first and the last letters must either
be N or B?
5. In how many ways can you seat two children and three adults in a row of five seats if the children are not to sit
together?
6. Find in how many ways can two admirals, three generals, and four lieutenants can be seated in a row of nine seats
of (a) the admirals sit at each end. (b) a general sit at each end and the lieutenants in consecutive seats.
7. A baseball tgam has 16 players. Suppose that the team has three star players: Ryan, Glenn and Manny, and that
they must be first, second and third, respectively. How many different batting orders are there for the team?
8. Seven boys and seven girls went to watch a movie. How many ways can they be seated if (a) the boys are to sit
together and so with the girls? (b) the boys and the girls are to sit alternately? (c) Grace and Joey are members of
the group and want to sit together all the time?
9. In how many ways can you sit 8 people on a round table (a) if there are no restrictions? (b) if two particular persons
want to sit next to each other?
10. Crisha has 5 different colored beads including purple and pink. In how many ways can she arrange the beads in a
string (a) if there are no restrictions? (b) so that the purple and pink beads are adjacent to each other?

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