A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
A. ¹²C₅ * 10
B. ¹²C₇ * 10
C. ¹²C₇ * ¹⁰C₅
D. 12 * ¹⁰C₅
A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior?
A. ²²C₁₀
B. ²²C₁₀ + 1
C. ²²C₉ + ¹⁰C₁
D. ²²C₁₀ – 1
Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. How many straight lines, including the first two, can be formed with these points?
A. 29
B. 32
C. 55
D. 30
A question paper had 10 questions. Each question could only be answered as true (T) of False (F). Each candidate answered all the questions, Yet no two candidates wrote the answers in an identical sequence. How many different sequences of answers are possible?
A. 20
B. 40
C. 512
D. 1024
Groups each containing 3 boys are to be formed out of 5 boys. A, B, C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?
A. 5
B. 6
C. 7
D. 8
In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together?
A. 120
B. 240
C. 360
D. 480
In a question paper, there are four multiple choice type questions, each question has five choices with only one choice for it’s correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
A. 19
B. 120
C. 624
D. 1024
A mixed doubles tennis game is to be played two teams(each consists of one male and one female) There are four married couples. No team is to consist a husband and his wife. What is the maximum number of games that can be played?
A. 12
B. 48
C. 36
D. 42
Three dice (each having six faces with each face having one number from 1 or 6) are ralled. What is the number of possible outcomes such that atleast one dice shows the number 2?
A. 36
B. 81
C. 91
D. 116
2 men and 1 woman board a bus of which 5 seats are vacant, one of these 5 seats is reserved for ladies. A woman may or may not sit on the seat reserved for ladies, In how many different ways can the five seats be occupied by these passengers?
A. 15
B. 36
C. 48
D. 60
