From 6 officers and 8 Jawans, in how many ways can 5 be chosen to include exactly 3 officers?

Required Number of ways = ^{6}C3 × ^{8}C2 = 6!/(3! ×3!) × 8!/(2! ×6!) = 20 × 28 = 560

- In how many different ways can the letters of the word ‘PADDLED’ be arranged?
- In how many different ways can the letters of the word ‘FLOWER’ be arranged in such a way that the vowels occupy only the odd positions?
- In how many ways can a group of 2 boys and 2 girls be made out of a total of 6 boys and 4 girls?
- In how ways can the selection be made so that a particular member is always excluded?
- What is the probability that four A’s come consecutively in the word ‘AMALGAMATION’
- In how many ways can 6 boys and 3 girls can be seated in a row so that they are in alternate position.
- In how many different ways can the letters of the word ‘CURIOES’ be arranged in such a way that the vowels occupy only the odd positions?
- In how many different ways can the letters of the word ‘NATURE’ be arranged in such a way that the vowels occupy only the odd positions?
- Find the number of words that can be formed by using all letters of the word ' PAINTING', if it starts with letter A and end with letter T.
- Find the quantity of methods of picking 4 cards from a set of 52 playing cards if four cards are of the same unit?

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