How many different collections of 30 coins can be chosen?
2006-07-17 09:31:24 · 8 answers · asked by retrodaisy1 1 in Science & Mathematics ➔ Mathematics
This question is incomplete.
2006-07-17 09:35:06 · answer #1 · answered by Will 6 · 2⤊ 0⤋
If you are not told how many coins are in the origional pile, the question is confusing.
It appears that each of the 30 coins I pick can be one of 3 coins {dime, penny, quarter}. That would mean 3^30 {three to the power of 30} possible piles.
If you're going by value of each pile... it gets very complex.
I would assume there is some missing data. If that was the full question, then there may be some that was not printed.
2006-07-17 10:55:47 · answer #2 · answered by adder_86 2 · 0⤊ 0⤋
You didnt say whether order is important, so Im going to assume that two dimes and a quarter is NOT the same as a quarter and two dimes.
If you could only pick up one coin, you could have 3 possible combinations: one penny(p), one dime(d), or one quarter(q).
Thats 3^1 combinations.
If you could only pick up two coins then you could have:
pp,pd,pq - dp, dd, dq - qp, qd, qq
Thats 3^2 combinations.
Lets test this. For 3 coins the combinations are
ppp, ppd, ppq, - pdp, pdd, pdq, - pqp pqd pqq
dpp, dpd, dpq, - ddp, ddd, ddq, - dqp dqd dqq
qpp, qpd, qpq, - qdp, qdd, qdq, - qqp qqd qqq
thats 9 * 3 or 3^3 or 27 combinations
For each coin you pick up you increase the power that 3 is raised to in order to determine the possible number of combinations.
If order DOES matter, so pd is not dp, then for 30 coins there are 3^30 combinations.
3^30 is approximately 2.0589 * 10^14 combinations
or about 205.89 trillion combinations.
If order does NOT matter its a different story. The number is much smaller. You didnt specify that it does or does not matter.
2006-07-17 09:47:02 · answer #3 · answered by Curly 6 · 0⤊ 0⤋
there are 3^30 variations - 3 types of coins, and 30 coins.
If it's n coins (more than 30) then it's 3^n
2006-07-17 09:35:03 · answer #4 · answered by asaaiki 3 · 0⤊ 0⤋
Depends how many coins are in the pile.
2006-07-17 09:35:55 · answer #5 · answered by Zaphod B 2 · 0⤊ 0⤋
You almost got it right Linwood.
When summing a series of numbers from 1 ... N, you use this equation.
(N * (N+1))/2
When N=31, the result is 496.
2006-07-17 12:08:59 · answer #6 · answered by Kookiemon 6 · 0⤊ 0⤋
That you are the third person and every person. Each person represent something or situation that is in relation to you
2006-07-17 09:42:46 · answer #7 · answered by Virtuous 3 · 0⤊ 0⤋
2.058911321x10^14 different possibilities
2006-07-17 09:48:34 · answer #8 · answered by SprinkleS 3 · 0⤊ 0⤋