Question

In how many ways can we give change for 100 using 1 rupee and 2 rupee coins? for example for 5 rs, we can give in three ways : (1,1,1,1,1) (1,1,1,2) (1,2,2)

Answer 1

Here we have to find out the number of ways we can distributed 100 rupees money to rupee 1 and rupee 2.

The simplest method is to find out the number of ways is to calculate the number of coins we use to break partitions. As example, the ways are

1, 1, 1,..........................................,1 (100 times 1)

1, 1, 1, ......................................, 1 and 2 (98 times 1 and 1 time 2)

1, 1, 1, ....................................., 1, 2 , 2 ( 96 times 1 and 2 times 2)

.............................

proceeding in this way, our last combination for taking the coins be

2, 2, 2, ........................, 2 (50 times 2)

So, here, we can find the numbers of ways by counting the number of 2 we took and is equal to 50 + 1 = 51.

Answer: 51 (ans.)

Answer 2

Answer:

Concept:

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Step-by-step explanation:

Given:

1 rupee and 2 rupee coins.

Find:

In how many ways can we give change for 100 using 1 rupee and 2 rupee coins.

example:  for Rs.5, we can give in three ways : (1,1,1,1,1) (1,1,1,2) (1,2,2).

Solution:

Here, we must determine the number of possible distributions of 100 rupees to Rupees 1 and 2.

calculating the number of coins we use to break divisions is the simplest technique to determine the number of possible solutions. Examples of these methods

1, 1, 1,..........................................,1 (100 times 1)

1, 1, 1, ......................................, 1 and 2 (98 times 1 and 1 time 2)

1, 1, 1, ....................................., 1, 2, 2 ( 96 times 1 and 2 times 2)

Continuing in this manner, our final arrangement for collecting the coins will be

2, 2, 2, ........................, 2 (50 times 2)

                                     $&=\frac{100}{2 ! \times 1 !}=\frac{100}{2 \times 1}=50$

So in 50 ways, we can give change for Rs.100 with the 1 rupee and 2 rupee coins.

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