Number of Questions:
15
level of difficulty:
Easy Q1. In how many ways can you select one or more books from a set of 7 books? Q2. In how many ways can a ten-question True/False test be answered? Q3. A club has 100 members. How many ways can the club form a committee of Q4. How many ways are there to deal a five-card hand consisting of three eight's and two sevens. Q5. In how many ways can 10 identical presents be distributed among 6 children so that each child gets at least one present? Q6. A man has 3 shirts, 4 trousers and 6 ties. What are the number of ways in which he can dress himself with a combination of all the three? Q7. How many 4 digit numbers larger than 5600 can be made using the digits 0, 1, 2, 5, 6, 8, 9 (no repetitions) Q8. If you have 2n socks in a drawer, n white and n black, and you reach in to choose 2 socks at random, Q9. How many ways can Janet select 3 of her 8 business suits to pack for a trip? Q10. How many different ways can a five-question true-false test can be answered? Q11. How many ways can 100 balls be put into three3 boxes with 50 balls going into one box and 25 into each of the other two? Q12. How many digits are required to number a book containing 200 pages? Q13. The number of ways in which 3 particular person X, Y, Z and 6 more persons can stand in a queue so that X always stands before Y and Y always before Z. Q14. How many ways can 8 people be seated around a circular table if Nicky and Monica insist on sitting together? Q15. There are three rooms in a motel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms?
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Q1> 7c1 +7c2+.....+7c7=127
Q2> 2^10
Q3> i> 100C3
ii> 100C97
iii> 1
iv> 100
Q4> 5!/(3! * 2!)= 10
Q5> (10+6-1) C (6-1)=15C5
Q6> 72
Q7> With 5 at 10^3 place...10^2 place can be filled in 3 ways... so total arrangements=60
and for nos greater than 5 taking 10^3 place in 3 ways..total no of arrangements=360
therefore, total numbers=420
Q8>i> 2nC2 ii> 2n*n iii> cant think of this...some one enlighten
Q9> 8C3
Q10> 2^5
Q11> (3!/2!)*(100C50)*(50C25)*(25C25)
Q12> 9+2*100+3*100=509
Q13> 7!
Q14> i> 6!*2! ii> 4! * 2! * 4!
Q15> 7!/(1!*2!*3!)
I know its coming.....and I know i can handle it the best....
n/a
Dear Abhi..........
Q13. The number of ways in which 3 particular person X, Y, Z and 6 more persons can stand in a queue so that X always stands before Y and Y always before Z.
Ans . 24x7!
Dear Abhi......
Q14. How many ways can 8 people be seated around a circular table if Nicky and Monica insist on sitting together?
b. if, in addition, George and Brent refuse to be seated together, how many ways can this be done?
Ans (b)
6! x 2! - 5! x 2! x 2!
Q5. In how many ways can 10 identical presents be distributed among 6 children so that each child gets at least one present?
a. 15C5 b. 16C6 c. 9C5 d. 610
Sol.
9C5
For Question 7,The answer will come as 588.Check it one more time.
case 1: 56_ _ -> unit and tenth place can be filled up in 5 x 4 = 20 diff ways
case 2: 5 8/9 _ _ -> unit , tenth and hundred place can be filled up in 5 x 4 x 2 = 40 diff ways
Case 3: _ _ _ _ -> unit ,tenth, hundred and thousand place can be filled up in 6 x 5 x 4 x 3 = 360 diff ways
Total possible numbers = 420
Q1. In how many ways can you select one or more books from a set of 7 books?
a. 63 b. 127 c. 7 d. 15
Solution:
The number of ways of selecting at least one out of n things is 2^n - 1 and hence the number of ways of selecting one or more books from a set of 7 books is 2^7 - 1 = 128 - 1 = 127
Thank You
Ravi Raja
n/a
Question 2: In how many ways can a ten-question True/False test be answered?
Solution:
Each question can be answered in either a True or False.
So, for each question there are two possible combinations. Hence the ten questions can be answered in 2^10 = 1024 ways.
Thank You
Ravi Raja
n/a
I dont think answer to 2 question is 2^10
The answer should be 3^10 since there are three ways of ttempting a question, i.e true , false or unanswered
The answer i think will 3^10 since there are 3 ways of attempting this questioni.e. true , false or not attempted
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