Job Roles

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) =( C37×C24 ) = 210.

Number of groups, each having 3 consonants and 2 vowels =210

Each group contains 5 letters.

Number of ways of arranging 5 letters among themselves = 5! = 120. 

Required number of words = (210 x 120) = 25200.

Since each number to be divisible by 5, we must have 5 0r 0 at the units place. But in given digits we have only 5.

So, there is one way of doing it.

Tens place can be filled by any of the remaining 5 numbers.So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

Required number of numbers = (1 x 5 x 4) = 20.

We may have (1 boy and 3 girls)or(2boys and 2 girls)or(3 boys and 1 girl)or(4 boys).

Required number of ways = (C16× C34) + C26×C24  + (C36× C14) + (C46)  

= (24+90+80+15) 

= 209.

Total number of flowers = (8+7+6) = 21.

Let E = event that the flower drawn is neither red nor green. 

= event taht the flower drawn is blue. 

--> n(E)= 7 

--> P(E)=  721=13 

Let S be the sample space. Then,
n(s) = number of ways of drawing 4 pearls out of 14

= C414 ways = 14×13×12×114×3×2×1= 1001

Let E be the event of drawing 4 pearls of the same colour.
Then, E = event of drawing (4 pearls out of 5) or (4 pearls out of 4) or (4 pearls out of 5)

  ⇒C15+ C44+ C15 = 5+1+5 =11

 P(E) = n(E)n(S)=111001=191  

 Required probability = 1-191=9091

The analogy here is like this: Veeru has 20 lt of petrol and he uses 1 lt per each day and consumes it in 20 days. If he uses 1.25 lt every day, in how many days it will be consumed?
We considered 1.25 lt here because it’s 25% more than 1 lt.

The answer would be  20/1.25=16 days.

After 10 days, the remaining food would be sufficient for the 1000 students for 20 more days

-->If 1000 more students are added, it shall be sufficient for only 10 days (as the no. of students is doubled, the days are halved).

(20 x 18) men can complete the work in in one day.

one man's one day work = 1/360

(18 x 15) women can complete the work in 1 day

1 woman's one day work = 1/270

So, required ratio = 1270:1360= 4:3