Permutation and Combination

Question 11

Out of 6 engineers and 4 doctors, how many groups of 4 professionals can be formed such that at least 1 engineer is always there?

• 129
• 109
• 229
• 209

Question 12

Out of 8 boys and 10 girls, how many groups of 5 boys and 6 girls can be formed?

• 11760
• 25200
• 720
• 120960

Question 13

In how many ways can the alphabets of the word ‘DERAIL’ be arranged so that the vowels come at the odd positions only?

• 12
• 18
• 24
• 36

Question 14

In how many different ways can the alphabets of the word ‘SCORING’ be arranged so that the vowels always come together?

• 120
• 720
• 240
• 1440

Question 15

The value of ⁷⁵C₂ is:

• 1215
• 2315
• 2775
• 1675

Question 16

How many distinguishable permutations of the letters in the word BANANA are there ?

• 720
• 120
• 60
• 360

Question 17

A relation r(A,B) in a relational database has 1200 tuples. The attribute A has integer values ranging from 6 to 20, and the attribute B has integer values ranging from 1 to 20. Assume that the attributes A and B are independently distributed. The estimated number of tuples in the output of σ_{(A>10)∨(B=18)}(r) is ____________.

• 820
• 1200
• 960
• 1000