A bag contains 8 coins of £1, 7 coins of 50p, 4 coins of 25p and 3 coins of 10p. How many different ways can we take 6 coins from the bag?
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To find the number of different ways we can take 6 coins from the bag, we can use a combination formula.
First, let's calculate the number of ways we can choose coins from each denomination.
For the £1 coins, we have 8 coins, and we can choose 0 to 6 coins from them. So, using the combination formula, the number of ways to choose coins from the £1 denomination is:
C(8,0) + C(8,1) + C(8,2) + C(8,3) + C(8,4) + C(8,5) + C(8,6)
Similarly, we can calculate the number of ways to choose coins from the 50p, 25p, and 10p denominations:
C(7,0) + C(7,1) + C(7,2) + C(7,3) + C(7,4) + C(7,5) + C(7,6)
C(4,0) + C(4,1) + C(4,2) + C(4,3) + C(4,4) + C(4,5) + C(4,6)
C(3,0) + C(3,1) + C(3,2) + C(3,3) + C(3,4) + C(3,5) + C(3,6)
To find the total number of ways to choose 6 coins from the bag, we multiply the number of ways to choose coins from each denomination:
Total Ways = (C(8,0) + C(8,1) + C(8,2) + C(8,3) + C(8,4) + C(8,5) + C(8,6)) * (C(7,0) + C(7,1) + C(7,2) + C(7,3) + C(7,4) + C(7,5) + C(7,6)) * (C(4,0) + C(4,1) + C(4,2) + C(4,3) + C(4,4) + C(4,5) + C(4,6)) * (C(3,0) + C(3,1) + C(3,2) + C(3,3) + C(3,4) + C(3,5) + C(3,6))
Evaluating the above expression will give us the number of different ways we can take 6 coins from the bag.