15 phones, 5 cell, 5 cordless, 5 corded, each are given numbers to establish the

Question

15 phones, 5 cell, 5 cordless, 5 corded, each are given numbers to establish the order they will be serviced.
A) what is the probability that all cordless phones are among the first ten serviced?
The answer given is [(5 choose 5)(10 choose 5)]/(15 choose 10)
I understand where (5 choose 5) comes from, this is the number of ways the five cordless phones can be chosen. I understand where (10 choose 5) comes from, that is the number of ways the remaining 5 phones can be chosen from the phones that remain, which would be ten since the 5 cordless have already been selected. And on the bottom, I understand where the (15 choose 10) comes from. This is the total number of ways ten phones can be chosen from 15. I am confused when the answer is worked out though. I keep getting (5!)(10!/[5!(5!)]) divided by (15!/[10!(5!)]), which should simplify to (10!10!)/(15!), but the answer has this (10!10!)/(5!15!). I cant figure out where that extra 5! is coming from.

Explanation / Answer

5 choose 5 is 1 not 5! dude :)

5 choose 5 = 5! / 5! 0! = 1

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.