Q1. What is the sum of all four-digit numbers that can be formed using the digits 1, 2, 5 and 8 if repetition not allowed? Q2. How many four–digit numbers can be formed if Q3. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made Q4. There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man? Q5. There are ten people available for appointment to a committee consisting of six people. The number of committees that cab be formed, if Krishna and James must be on the committee is Q6. There are 5 bottles of sheery and each has their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the correct bottle? Q7. Three men and 3 women are sitting at a round table, each women being flanked by two men and vice versa. How many different seating arrangements are possible such that in no arrangement every man is flanked by the same women? 8. Using the letters of the word FACTOR (without repetitions), how many four-letter code words can be formed: 9. The number of ways in which 3 balls of different colors can be put in 3 boxes labeled A, B, C such that at most one box is empty. Q10. In how many ways can five boys and five girls be seated in a row if Q11. One bag contains 4 colored marbles, and another bag contains 4 colored marbles. None of the 8 marbles are the same color. If a person reaches into the first bag and pulls out two marbles, then reaches into the second bag and pulls out two marbles, the number of possible color combination is Q12. A school has scheduled three volleyball games, two soccer games, and four basketball games. You have a ticket allowing you to attend three of the games. In how many ways can you go to two basketball games and one of the other events? Q13. There are 100 articles numbered n1 , n2, . . . . . .n100. They are arranged in all possible ways. How many arrangements would be there in which n28 will always be before n29 . Q14. Three brothers and 3 sisters are lining up for a picture. How many arrangements are there: Q15. Lotto 6-49 is a lottery in which one selects 6 numbers from 1 to 49. How many ways can this be done? END |
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Q1. What is the sum of all four-digit numbers that can be formed using the digits 1, 2, 5 and 8 if repetition not allowed?
a. 106656 b. 106756 c. 147166 d. 105466
Sol.
the sum of all four-digit numbers that can be formed using the digits 1, 2, 5 and 8 if repetition not allowed
= 6666 x 16 = 106656
Q2. How many four–digit numbers can be formed if
a. There are no restrictions? (Zero is not the first digit.)
b. Zero cannot be the first digit and no digit can be repeated?
Sol.
a. 9 x 103 = 9000
b. 9 x 9 x 8 x 7 = 4536
Q2. How many four–digit numbers can be formed if
c. Zero cannot be the first digit, no digit can be repeated, and each number formed must be even?
Sol.
if units digit is zero, total number of 4-digit numbers = 9 x 8 x 7 x 1 = 504
if units digit is 2, 4, 6 or 8, total number of 4-digit numbers = 8 x 8 x 7 x 4 =1792
total numbers = 2296
Q3. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made
Sol.
10C1 x 9C5 = 1260
Q4. There are five women and six men in a group. From this group a committee of 4 is to be chosen. How many different ways can a committee be formed that contain three women and one man?
Sol.
5C3 x 6C1 = 60
Q5. There are ten people available for appointment to a committee consisting of six people. The number of committees that cab be formed, if Krishna and James must be on the committee is
Sol.
8C4 = 70
8. Using the letters of the word FACTOR (without repetitions), how many four-letter code words can be formed:
a. starting with R?
b. with vowels in the two middle positions?
c. With only consonants?
d. With vowels and consonants alternating?
Sol.
a. starting with R = 5 x 4 x 3 = 60
b. with vowels in the two middle positions = 4 x 2 x 1 x 3 = 24
c. With only consonants = 4 x 3 x 2 x 1 = 24
d. With vowels and consonants alternating = 2 x 4 x 2 x 3 x 1 = 48
9. The number of ways in which 3 balls of different colors can be put in 3 boxes labeled A, B, C such that at most one box is empty.
a. 6 b. 18 c. 24 d. 36
Sol.
case i. no box is empty = 6 ways
case ii. one box is empty = 3! x 3C1 x 2C2 = 18 ways
ans. 24 ways
Q10. In how many ways can five boys and five girls be seated in a row if
a. Boys and girls are seated alternately?
b. Boys sit side by side and girls sit side by side?
c. One of the girls, Sue, must be seated on the left end?
Sol.
a. Boys and girls are seated alternately = 2 x 5! x 5!
b. Boys sit side by side and girls sit side by side = 2 x 5! x 5!
c. One of the girls, Sue, must be seated on the left end = 9!
Q10. In how many ways can five boys and five girls be seated in a row if
a. Boys and girls are seated alternately?
b. Boys sit side by side and girls sit side by side?
c. One of the girls, Sue, must be seated on the left end?
Sol.
a. Boys and girls are seated alternately = 2 x 5! x 5!
b. Boys sit side by side and girls sit side by side = 2 x 5! x 5!
c. One of the girls, Sue, must be seated on the left end = 9!
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