From 4 officers and 8 jawans in how many ways can 6 be chosen

(i) to include exactly one officer

(ii) to include at least one officer?

Asked by Aaryan | 1 year ago |  33

##### Solution :-

Given:

Total number of officers = 4

Total number of jawans = 8

Total number of selection to be made is 6

(i) to include exactly one officer

Number of ways = (no. of ways of choosing 1 officer from 4 officers) × (no. of ways of choosing 5 jawans from 8 jawans)

= (4C1) × (8C5)

By using the formula,

nCr = $$\dfrac{ n!}{r!(n – r)!}$$

(ii) to include at least one officer?

Number of ways = (total no. of ways of choosing 6 persons from all 12 persons) – (no. of ways of choosing 6 persons without any officer)

12C6 – 8C6

By using the formula,

nCr = $$\dfrac{ n!}{r!(n – r)!}$$

= (11×2×3×2×7) – (4×7)

= 924 – 28

= 896 ways

The required no. of ways are 224 and 896.

Answered by Sakshi | 1 year ago

### Related Questions

#### How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

#### Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

#### How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’,

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

(i) 4 letters are used at a time

(ii) all letters are used at a time

(iii) all letters are used but first letter is a vowel ?