Find the total number of ways in which a beggar can be given at least one rupee from four 25paise coins,three 50paise coins & 2 one rupee coins ? (1rupee=100paise)

Question

Christopher Axton · Accepted Answer

98

There are nine coins in total. I can choose to give one, some, or all of the coins to the beggar. Since each choice for each coin is a yes/no, I can use #2^x# to figure out the total number of combinations. #2^7=128# ~~~~~ To check this, let's say we have 3 coins called A, B, C. We should have #2^3=8# ways to give the coins: A B C AB BC AC ABC none ~~~~~ How many ways out of the 128 makes a rupee? One way to do this is to count the number directly and the other is to figure out how many ways we don't make a rupee and subtract that from 128. I think I'll approach this by not going over 1 rupee. What are the different coin combinations that will keep us under? Each of these, being a combination, will fall under this general equation: #C_(n,k)=(n!)/((k!)(n-k)!)# with #n="population", k="picks"# 1 X 25 paise 2 X 25 paise 3 X 25 paise 1 X 50 paise 1 X 50 paise + 1 X 25 paise We can evaluate each of these: 1 X 25 paise #C_(4,1)=(4!)/((1!)(4-1)!)=(4!)/(3!)=24/6=4# 2 X 25 paise #C_(4,2)=(4!)/((2!)(4-2)!)=(4!)/((2!)(2!))=24/4=6# 3 X 25 paise #C_(4,3)=(4!)/((3!)(4-3)!)=(4!)/((3!)(1!))=24/6=4# 1 X 50 paise #C_(3,1)=(3!)/((1!)(3-1)!)=(3!)/((1!)(2!))=6/2=3# 1 X 50 paise + 1 X 25 paise #C_(3,1)C_(4,1)=3xx4=12# Let's add them up: #4+6+4+3+12=29# Finalizing up We start with 128 ways to hand out coins. We need to subtract 1 to account for not having any coin, then another 29 for handing out coins that are insufficient to reach 1 rupee. This leaves us with: #128-1-29=98#

Anthony Arnold · Answer

undefined To find the total number of ways to give at least one rupee to the beggar:

1. Use at least one 1 rupee coin: 1 way
2. Use one 1 rupee coin and any combination of 25 paise and 50 paise coins: 
   - 1 one rupee coin + 1 of 25 paise coin + 3 of 50 paise coin = 1 way
   - 1 one rupee coin + 2 of 25 paise coin + 2 of 50 paise coin = 1 way
   - 1 one rupee coin + 3 of 25 paise coin + 1 of 50 paise coin = 1 way
   - 1 one rupee coin + 4 of 25 paise coin = 1 way
3. Use two 1 rupee coins and any combination of 25 paise and 50 paise coins:
   - 2 one rupee coins + 2 of 25 paise coin + 1 of 50 paise coin = 1 way
   - 2 one rupee coins + 3 of 25 paise coin = 1 way

Total number of ways = 1 (from case 1) + 4 (from case 2) + 2 (from case 3) = 7 ways.

Find the total number of ways in which a beggar can be given at least one rupee from four 25paise coins,three 50paise coins &amp; 2 one rupee coins ? (1rupee=100paise)

Find the total number of ways in which a beggar can be given at least one rupee from four 25paise coins,three 50paise coins & 2 one rupee coins ? (1rupee=100paise)