Math Is Fun Forum

shivusuja

Member

Registered: 2006-09-14

Posts: 56

Permutation And Combination

Please help me with this 3 sums as tomorrow examination is there

1. Find the number of ways of selecting 9 balls from 6 red balls 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

2.  Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination

3.  In how many ways can one select a cricket team of 11 from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers.

Thank you

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Permutation And Combination

1. [Mine is wrong. See Pi Man’s solution below. ]

Last edited by JaneFairfax (2007-09-18 21:44:15)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Permutation And Combination

2. After an ace has been picked, the other four cards can be from any of the 48 non-ace cards in the deck, so there are [sup]48[/sup]C[sub]4[/sub] = 194 580 ways of selecting these. And there are 4 aces. So the total number of selections required is 4 × 194 580 = 778 320.

Last edited by JaneFairfax (2007-09-18 03:52:54)

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Permutation And Combination

I'm reading question #1 differently than Jane.   I think shivusuja is asking how many ways can you select 9 balls with the requirement that you have 3 of each color.   But I've been wrong before!

If 3 balls of each color are right, then they are 20 ways to select 3 red balls (6 choose 3) and 10 ways to choose blue and 10 ways to choose white (5 choose 3).   So that would mean 2000 different ways.  This doesn't take into consideration the order of which the balls drawn.

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Permutation And Combination

#3.   Again, I'm not sure if I'm reading this correctly but...

You must select 4 bowlers from a group of 5.    That's (5 choose 4) and is equal to 5.
You must select an additional 7 players from the remaining 12.   (12 choose 7) =   792.

5*792=3960 is what I come up with.