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How did they find those?
1- 4 students have to be chosen 2 girls as captain and vice captain and 2 boys as captain and vice captain of the school. there are 15 girls and 12 boys. In how many ways can they be chosen if sunita (girl) is sure to be captain?
Ans 1848.
2-A prof prepares a test. She gives 5 objective type questions out of which 4 have to be answered. Find the total way in which they can be answered if the first 2 questions have 2 choices and the last 3 have 4 choices.
A: 816
3-How many five digit numbers are there with distinct digits?
Ans:27216
4-In how many ways can 15 students be seated in a row such that the most 2 talkative students never sit together?
Ans 14! *13
5-Find the number of words which can be formed by using the letter of the word EQUATION if each word has to start with a vowel?
Ans: 25200
6-How many five digit numbers can be formed using the digits 0,2,3,4,5 when repetition is allowed such that the number formed is divisible by 2 or 5 or both?
Ans: 1500
1. Sun + Vc and 2 boys
ways = 1 x 14 x 12 x 11 = 1848
2. 2x{2 x 4×4x4} + 3 x{2×2x4×4} = 448 (leaving out a different question each time)
3. 9 x 9 x 8 x7 x6 (no zero in first place)
4. unrestricted total – together
15! – 2!x14! (treat as one unit which can be arranged in 2! ways)
= 15 x 14! – 2 x 14!
= 13 x 14!
5. 5 x 7! =25200
6. must end in 2,5 or 0
can’t start with 0
4×5x5×5x3 = 1500
its all high school mathematics.
refer to maths & stats by chitale joshi.
i know how to do all of this. but i can’t explain here as i am running out of time. You can email them to me. I have bachelor degree in math. They are very easy and deal with probability stuff material.
Pl ask one question at a time.
For q1,
there are 15 girls and 12 boys
Since one girl Sunita hs to be the captain, there are 14 girls left to be choosen as vice captaion, i.e in 14 ways.
For boys
Captain be choosen in 12 ways.
After choosing a captain, 11 boys are left. hence, a vice captain can be choosen in 11 ways.
Therefore, from the lot 2girls and 2 boys can be choosen in 14x 12x 11= 1848 ways.