Question

A bag contains 6 five rupee coins, 8 two rupee coins and 4 one rupee coins. If three coins are chosen from the bag then the probability of the sum of the three coins will be maximum possible is

Answer 1

Answer:

15 is the answer

Since there are 6 five rupee coins their total amount will be 30

However there are 8 two rupee coins thier total will be only 16

Therefore 5 rupee coins give more amount

Which implies 3 times taking 5 rupee coin gives us 15

Step-by-step explanation:

Answer 2

The probability of the maximum sum of the three coins is  $\frac{5}{204}$

Given:

No of five rupee coins= 6 = 6*5 = 30rs

No. of two rupee coins= 8 = 8*2= 16rs

No. of one rupee coins= 4 = 4*1 = 4rs

To Find:

Maximum sum when three coins are chosen from the bag.

Solution:

The bag contains 6 five rupee coins, 8 two rupee coins, and 4 one rupee coins.

Total number of coins = 18

Select three coins from the bag: 18C3=$\frac{18!}{3!(18-3)!}$=$\frac{18!}{3!*15!}$=$816$

The Sum of three coins will be maximum when all the three coins selected are five rupees.

Therefore,

Select three coins of rupee five=6C3=$\frac{6!}{3!(6-3)!}$=$\frac{6!}{3!*3!}$=$20$

Probability of selecting three coins with maximum sum =20/816 = $\frac{5}{204}$

Hence, the probability of getting the maximum sum is 5/204.

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