Permutation & Combination:
Q: How many ways can 3 books be arranged on a shelf?
Answer: 3!=6Q: How many ways can 5 people sit in a row?
Answer: 5!=120Q: How many ways can 2 letters be chosen from A, B, C, D?
Answer: C(4,2)=6Q: How many ways can 2 letters be arranged from A, B, C, D?
Answer: P(4,2)=12Q: In how many ways can 4 digits be formed using 1, 2, 3, 4 without repetition?
Answer: 4!=24Q: How many 3-digit numbers can be formed using digits 1, 2, 3, 4 with repetition?
Answer: 4^3=64Q: How many 3-digit numbers can be formed using digits 1, 2, 3, 4 without repetition?
Answer: P(4,3)=24Q: How many ways can a committee of 2 men and 2 women be chosen from 5 men and 4 women?
Answer: C(5,2)\times C(4,2)=10\times 6=60Q: How many ways can 6 people sit around a circular table?
Answer: (6-1)!=120Q: How many ways can 3 boys and 2 girls be seated in a row if girls must sit together?
Answer: Treat girls as 1 unit → 4!\times 2!=48Q: How many ways can the letters of the word DELHI be arranged?
Answer: 5!=120Q: How many ways can the letters of the word BANANA be arranged?
Answer: \frac{6!}{3!2!}=60Q: How many ways can 10 students be divided into 2 groups of 5 each?
Answer: \frac{C(10,5)}{2}=126Q: How many ways can 4 people be chosen from 10?
Answer: C(10,4)=210Q: How many ways can 3 people be chosen from 10 and arranged in a line?
Answer: P(10,3)=720Q: How many ways can 5 cards be chosen from a deck of 52?
Answer: C(52,5)=2,598,960Q: How many ways can 5 cards be chosen and arranged in order?
Answer: P(52,5)=311,875,200Q: How many ways can 4 balls be placed into 3 boxes if boxes can be empty?
Answer: 3^4=81Q: How many ways can 6 people be arranged in a circle if rotations are considered same?
Answer: (6-1)!=120Q: How many ways can 6 people be arranged in a circle if rotations and reflections are considered same?
Answer: (6-1)!/2=60