How many batting orders are possible for the Indian cricket team if th...
The condition is that we have to count the number of natural numbers not more than 4300.
The total possible numbers with the given digits = 5x5 x5 x5 = 625 - 1 = 624.
Subtract form this the number of natural number greater than 4300 which can be formed from the given digits =1x 2x 5x5 -1 =49 .
Hence, the required number of numbers = 624 - 49 = 575.
View all questions of this test
How many batting orders are possible for the Indian cricket team if th...
Explanation:
Total number of players to choose from:
- Total players in the squad = 15
Given condition:
- Sachin Tendulkar is always chosen in the batting order
Number of remaining players to choose from:
- Remaining players = Total players - Sachin Tendulkar
- Remaining players = 15 - 1
- Remaining players = 14
Calculating the number of batting orders:
- Since Sachin Tendulkar is always chosen, the batting order will consist of Sachin Tendulkar and 10 other players
- Number of ways to arrange 10 players = 10!
- Number of ways to arrange Sachin Tendulkar and 10 other players = 1 * 10!
Total number of batting orders:
- Total number of batting orders = 1 * 10!
- Total number of batting orders = 10!
Calculating the total number of batting orders:
- Total number of batting orders = 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
- Total number of batting orders = 3,628,800
Therefore, the total number of batting orders possible for the Indian cricket team, given that Sachin Tendulkar is always chosen, is 3,628,800 or 1001 x 11!