Combinatorics | Number Theory Answers

Q2 An investigator interviewed 100 students to determine preference for three drinks: Milk(M), Coffee(C), Tea(T). He reported the following: 10 students had all the three drinks M,C,T; 20 had M&C: 30 had C&T; 25 had M&T; 12 had M only; 5 had C only & 8 had T only. Enumerate how many did not take any of the drink.

out of 250 candidates who failed in an examination, it was revealed that 128 failed in mathematics, 87 in physics and 134 in aggregate, 31 failed in mathematics and in physics 54 failed in the aggregate and in mathematics, 30 failed in the aggregate and in physics. find how many candidates failed.
1 in all the three subjects. 2. in mathematics but not in physics. 3. in the aggregate but not in mathematics 4. in physics but not in the aggregate or in mathematics 5. in the aggregate or in mathematics, but not in mathematics

James brought fewer donuts than two dozen of donuts. He wants to evenly share them among 2,3,4 people. No matter how many people he shares them with he Aways have one left over. How many did he buy? What numbers goes in to 24 when factored with 2,3,4 gives remainder of 1

if factorial r = 24 . what is value of r ?

how many numbers of five digits each can be made from the digits 1,2,3,4,5,6,7,8,9, where each number contains exactly one even digit and no digit is used more than once

Let S={a,b}.how many elements does the power set 2s contain?

Let s={1,2,3} .how many subsets does s contain?

i have problems with iota how to solve this for example Evaluate:- i50(50 at top right corner as a power)

Add two digits after 16 in such a way that the new 4-digit number is divisible by 3,4 and is the lowest one.Find out that new 4-digit number.

in how many ways can a committee of 5 be formed from agroup of 11 people consisting of 4 teachers and 7 students if
- there is no restriction in the selection?
- the committee must include exactly 2 teachers?