A bag contain 3 white, 2 green and 5 yellow tokens. 3 tokens are drawn

1.	A bag contain 3 white, 2 green and 5 yellow tokens. 3 tokens are drawn in such a way that not more than 2 tokens are yellow. Find the number of ways to do the operation.1. 1102. 1203. 1354. 150
Answer» Correct Answer - Option 1 : 110 Concept: The ways of arranging n different things = n! The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\) The no. of ways of arranging the n arranged thing and m arranged things together = n! × m! The number of ways for selecting r from a group of n (n > r) = nCr To arrange n things in an order of a number of objects taken r things = nPr Calculation: The operation can be done = (No token drawn is yellow) or (2 non-yellow token and 1 yellow token) or (1 non-yellow token and 2 yellow token) Non-yellow tokens = 3 + 2 = 5 Ways of selecting of 3 non-yellow tokens out of 5 = 5C3 = 10 Ways of selecting of 2 non-yellow tokens out of 5 = 5C2 = 10 Ways of selecting of 1 non-yellow token out of 5 = 5C1 = 5 Ways of selecting of 2 yellow tokens out of 5 = 5C2 = 10 Ways of selecting of 1 yellow token out of 5 = 5C1 = 5 ∴ The total number of ways N = 10 + (10 × 5) + (5 × 10) N = 10 + 50 + 50 = 110

A bag contain 3 white, 2 green and 5 yellow tokens. 3 tokens are drawn in such a way that not more than 2 tokens are yellow. Find the number of ways to do the operation.1. 1102. 1203. 1354. 150

Answer» Correct Answer - Option 1 : 110

Concept:

The ways of arranging n different things = n!
The ways of arranging n things, having r same things and rest all are different = \(\rm n!\over r!\)
The no. of ways of arranging the n arranged thing and m arranged things together = n! × m!
The number of ways for selecting r from a group of n (n > r) = nCr
To arrange n things in an order of a number of objects taken r things = nPr

Calculation:

The operation can be done = (No token drawn is yellow) or (2 non-yellow token and 1 yellow token) or (1 non-yellow token and 2 yellow token)

Non-yellow tokens = 3 + 2 = 5

Ways of selecting of 3 non-yellow tokens out of 5 = 5C3 = 10

Ways of selecting of 2 non-yellow tokens out of 5 = 5C2 = 10

Ways of selecting of 1 non-yellow token out of 5 = 5C1 = 5

Ways of selecting of 2 yellow tokens out of 5 = 5C2 = 10

Ways of selecting of 1 yellow token out of 5 = 5C1 = 5

∴ The total number of ways N = 10 + (10 × 5) + (5 × 10)

N = 10 + 50 + 50 = 110