QBM080
Q1. How many numbers of ‘n’ digits can be made with the non zero digit in which no two consecutive digits are the same?
Q2. In how many ways can a ten-question True/False test be answered?
Q3. In an election, there are 6 candidates for president, 4 for vice president, 5 for secretary, and 6 treasurer. How many different possible outcomes are there for the election?
Q4. How many 4-letter words can be made from the letters of MISSISSIPPI if the words must begin with an S and letters cannot be repeated?
Q5. A local delivery company has three packages to deliver to three different homes.
If the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?
Q6. 5 different fruits are to b given to 8 children. In how many ways can u do distribution if there is no restriction on number of fruits with one child?
Q7. Find the number of sides and number of diagonals of a hexagon?
a. 210 b. 15 c. 6 d. 9
Q8. Badri has 9 pairs of dark Blue socks and 9 pairs of Black socks. He keeps them all in a same bag. If he picks out three socks at random what is the probability he will get a matching pair?
Q9. How many different collections of six integers are there (duplicates allowed), where each integer is between 0 and 8, and the sum equals 20? (Use Inclusion/Exclusion).
Q10. How many different numbers which are smaller than 2x108 can be formed using the digits 1 and 2 only?
a. 766 b. 94 c. 92 d. 126
Q11. How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?
Q12. Several teams take part in a competition, each of which must play one game with all the other teams. How many teams took part in the competition if they played 45 games in all?
a. 5 b. 10 c. 15 d. 20
Q13. There are 4 letters and 4 envelopes. In how many ways can wrong choices be made?
a. 43 b. 4! – 1 c. 16 d. 44 – 1
Q14. In how many ways one white and one black rook can be placed on a chessboard so that they are never in an attacking position?
a. 64 x 50 b. 64 x 49 c. 63 x 49 d. None of these
Q15. If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?
END
Q1. How many numbers of ‘n’ digits can be made with the non zero digit in which no two consecutive digits are the same?
Sol.
9x8x8x8x8............................(n - 1)th times
= 9 x 8n - 1
Q2. In how many ways can a ten-question True/False test be answered?
Sol.
each question has ethier ture or false answer.
total ways = 210
Q3. In an election, there are 6 candidates for president, 4 for vice president, 5 for secretary, and 6 treasurer. How many different possible outcomes are there for the election?
Sol.
= 6 x 4 x 5 x6
= 720
Q4. How many 4-letter words can be made from the letters of MISSISSIPPI if the words must begin with an S and letters cannot be repeated?
Sol.
only 4 diff letters in word MISSISSIPPI.
4-distinct letters word with using S, I, P and M and beging with S.
1 x 3 x 2 x 1 = 6
Q5. A local delivery company has three packages to deliver to three different homes.
If the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?
Sol.
total ways = 3 x 2 x 1 = 6
but only 1 way is right.
ans. 6 - 1 = 5
Q6. 5 different fruits are to b given to 8 children. In how many ways can u do distribution if there is no restriction on number of fruits with one child?
Sol.
8 + 5 - 1C5 - 1 = 12C4 = 495
Q7. Find the number of sides and number of diagonals of a hexagon?
a. 210 b. 15 c. 6 d. 9
Sol.
number of diagols = 6C2 - 6 = 9
Q8. Badri has 9 pairs of dark Blue socks and 9 pairs of Black socks. He keeps them all in a same bag. If he picks out three socks at random what is the probability he will get a matching pair?
Sol.
total ways = 18C3 = 1836
favorable way
all three ethier blue or black = 2 x 9C3 = 336
two black and one blue or two blue and one black = 2 x 9C2 x 9C1 = 648
probability = 984/1836 = 82/ 153
Q11. How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels, if all the letters are different?
Sol.
12C4 x 4C3 x 7! = 9979200
Q2. 10C2
Q3. In an election, there are 6 candidates for president, 4 for vice president, 5 for secretary, and 6 treasurer. How many different possible outcomes are there for the election?
ANS: 6C1 x 4C1 x 5C1 x 6C1
Q4. How many 4-letter words can be made from the letters of MISSISSIPPI if the words must begin with an S and letters cannot be repeated?
ANS: 6