Question: 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?

• 1. 29
• 2. 32
• 3. 55
• 4. 30

Question: 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?

• 1. ²²C₁₀
• 2. ²²C₁₀ + 1
• 3. ²²C₉ + ¹⁰C₁
• 4. ²²C₁₀ – 1

Question: 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?

• 1. ¹²C₅ * 10
• 2. ¹²C₇ * 10
• 3. ¹²C₇ * ¹⁰C₅
• 4. 12 * ¹⁰C₅

Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group?

• 1. 300
• 2. 450
• 3. 600
• 4. 750

Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?

• 1. 300
• 2. 600
• 3. 750
• 4. 900

Question: Find the number of ways of arranging the letters of the word “MATERIAL” such that all the vowels in the word are to come together?

• 1. 720
• 2. 1440
• 3. 1860
• 4. 2160

Question: The number of new words that can be formed by rearranging the letters of the word ‘ALIVE’ is__________?

• 1. 24
• 2. 23
• 3. 119
• 4. 120

Question: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?

• 1. 20
• 2. 54
• 3. 42
• 4. 60

Question: The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.

• 1. 4000
• 2. 2160
• 3. 4320
• 4. 5300

Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?

• 1. 4800
• 2. 5760
• 3. 2880
• 4. 15000