Probability.....

Question

There are $65$ currency notes of RS $1000$ and $35$ currency notes of RS $500$ in a safe. If $4$ notes are selected randomly find that total amount obtained is at least Rs $4000$

It's answer is $0.1727$ The method I tried is $1-($total amount is not $4000)$ but couldn't get the desired answer.

Answer 1

Hints:

• $4000=4 \times 1000$ so in this case at least $4000$ is equivalent to exactly $4000$
• you do not need to subtract from $1$
• you do need to take account of sampling without replacement

Answer 2

The only way to get RS $4000$ with four notes is to pick out four RS $1000$ notes.

So choose $4$ of the $65$ RS $1000$ notes (how many ways?) and divide by the total number of ways you can choose four notes (how many ways?)

Spoiler:

${65 \choose 4} / {100 \choose 4}$