9. How many ways can three balls be chosen randomly from a bag of 8 red balls, 3 white balls and 9 blue balls if a all are red b. all are white c. two balls are red and one is white d. one ball for each colour
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.
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ten points. How many triangles can be drawn using these points as vertices?
9. How many ways can three balls be chosen randomly from a bag of 8 red balls, 3 white balls
and 9 blue balls if
a all are red
b. all are white
c. two balls are red and one is white
d. one ball for each colour
SMO025 2019/2020
Tutorial 9 : Permutation and Combination
10. The parent-teacher'sassociation committee of a school consisting of 6 members is to be formed
from 7 parents, 4 teachers and the principal, In how many ways can the committee be formed
so that it includes
a. the principal
b. exactly 3 parents
c. not more than 3 parents
11. There are 6 routes for traveling from A to B and 4 routes for traveling from B to C, Find the
number of ways a person can travel
a from A to C via B
b. from A to C and back to A via B in each trip
c. from A to C and back to A via Bin each tr ip without taking the same route more than one e.
12. For a badm inton doubles game, 2 players are chosen from among 5 male and 3 female players
to represent a elub. In how many ways can this doubles pair be selected if
a the team is amixed double, comprising one male player and one female player
b. the team is eithera male pair or a female pair and no mixed pmir is allowed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6752982a-41ff-400d-abe9-82e06aeca691%2F8e890f77-10ce-4964-9ce5-ef5241da0d8d%2Ft9zpwls_processed.jpeg&w=3840&q=75)
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*目
Tutorial 9: Permutation and Combination
Tutorial 9: Pemutat ion and Combination
1. Six volumes of encyclopedia are placed on a shelf In how many different ways can they be
arranged? Two of the volumes are bound in red. In how many ways can the books now be
arranged if the two red volumes are not next to each other?
2. There are eight competitors in the final of a 200m race. The first three competitorsto complete
the course will all receive medals. Calculate the number of different possible groups of medal
winners.
3. Given the word PERINGKAT,
a. how many arrangements can be made if all the letters are used ?
b. In how many ways can 4 letters be chosen and arranged beginning with the letter N ?
c. In how many ways can 4 letters be chosen and arranged containing the letter A ?
4. Given the digits 6, 7, 8, 9,
a. how many four number digits can be formed if there's no repetition of digits ?
b. how many four number digits can be fomed if repetition is allowed ?
c. how many four number digits between 6000 and 7000 can be formed if repetition is allowed?
5. Four married couples bought 8 tickets in a row for a concert. In how many ways can they be
seated if
a. there is no restrictions
b. each couple sits together
c. all the men are seated together with all the women on their right ?
6. Eight people, of whom P, Q, and R are three of them, arrange themsel ves in a straight line. In
how many ways can this be done if
a. Pand Q must not be together,
b. P, Q and R must not be together.
7. Find the number of selections of 4 letters that can be made from the let ters in the word
INTEGRAL How many of these selections do not contain a vowel?
8. Ten distinet points each I cm apart are collincar. One other point is not collinear with these
ten points. How many triangles can be drawwn using these points as vertices?
BO 00
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