SOLUTION: There are five balls that must be played in a game. Two of the balls are signed
balls and must be played either first or last. Each ball can only be played once.
How many possibl
Algebra.Com
Question 252789: There are five balls that must be played in a game. Two of the balls are signed
balls and must be played either first or last. Each ball can only be played once.
How many possible orderings (permutations) can the balls be played?
A) 2 B) 12 C) 60 D) 120 E) 3125
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
each signed ball have to be played in the first or last game so they are fixed at 2 games, one for each.
the other 3 balls can be in games 2,3,4 in any order.
all balls can be played in one game only.
the number of permutations for the 3 unsigned balls is 3! = 3*2*1 = 6.
the two signed balls can be played in the first or last position only.
the number of permutations for the signed balls is 2!.
the total order of permutations is 2 * 6 = 12.
that's 2 permutations for the signed balls times 6 permutations for the unsigned balls.
here's how it works.
let a,e be the signed balls.
let b,c,d be the unsigned balls.
your possible permutations for games 1,2,3,4,5 are:
a,b,c,d,e
a,b,d,c,e
a,c,b,d,e
a,c,d,b,e
a,d,b,c,e
a,d,c,b,e
e,b,c,d,a
e,b,d,c,a
e,c,b,d,a
e,c,d,b,a
e,d,b,c,a
e,d,c,b,a
RELATED QUESTIONS
There are 8 blue balls, 8 yellow balls and 8 red balls of the same type inside a sack.... (answered by ikleyn)
6. The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and... (answered by Boreal)
The 20 balls in a box (5 Balls with A on them, 10 Balls with B on them, 7 Balls with C on (answered by solver91311)
A bag contains six white, five red, and four balls. If six ball are drawn, find the... (answered by stanbon)
The 20 balls in a box as shown above have either 0 (blank), 1, or 2 letters on them. If... (answered by Edwin McCravy)
There are 9 balls put inside a bag. The balls are either white or black! How many balls... (answered by Edwin McCravy)
If five balls are drawn from a bag containing six green balls, eight blue balls, and ten... (answered by Boreal)
Two friends A and B play a checkers match which will end when one player has won three... (answered by robertb,ikleyn)
Balls are printed in a pattern. Every 18th ball has stripes, every 15th ball has polka... (answered by KMST)