Tag: math & puzzles

To solve this question, the user needs to understand basic arithmetic, combinations, and the concept of counting. The boy starts with Rs 2 and can win or lose Re 1 at a time. He can lose only 5 times and is out of the game if he earns Rs 5. We need to find the number of ways in which this is possible.

Let's consider the possible outcomes for the boy's first 5 games:

• He can win all 5 games, which would result in him earning Rs 7.
• He can win 4 games and lose 1 game, which would result in him earning Rs 6.
• He can win 3 games and lose 2 games, which would result in him earning Rs 5.
• He can win 2 games and lose 3 games, which would result in him earning Rs 4.
• He can win 1 game and lose 4 games, which would result in him earning Rs 3.
• He can lose all 5 games, which would result in him earning Rs 2.

We can count the number of ways in which each outcome is possible using combinations. For example, the number of ways for the boy to win 4 games and lose 1 game can be found by calculating the number of ways to choose 4 games out of 5 to win, which is 5 choose 4, or ${5 \choose 4} = 5$. The number of ways for him to win all 5 games can be found by calculating the number of ways to choose 5 games out of 5 to win, which is 5 choose 5, or ${5 \choose 5} = 1$. We can use similar logic to count the number of ways for each outcome.

Let's list out the number of ways for each outcome:

• He can win all 5 games: 1 way
• He can win 4 games and lose 1 game: ${5 \choose 4} = 5$ ways
• He can win 3 games and lose 2 games: ${5 \choose 3} = 10$ ways
• He can win 2 games and lose 3 games: ${5 \choose 2} = 10$ ways
• He can win 1 game and lose 4 games: ${5 \choose 1} = 5$ ways
• He can lose all 5 games: 1 way

To find the total number of ways for the boy to earn Rs 5 or less, we just need to add up the number of ways for each outcome: 1 + 5 + 10 + 10 + 5 + 1 = 32

Therefore, the answer is:

The Answer is: C) 16