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Answer :
Final answer:
To calculate the number of ways in which 9 children can be divided into groups of 2 and 3, we can use combinatorics. The number of ways to choose 2 children out of 9 is C(9, 2) and the number of ways to choose 3 children out of 7 is C(7, 3). Therefore, the total number of ways is C(9, 2) x C(7, 3), which is 36 x 35 = 126 ways.
Explanation:
To calculate the number of ways in which 9 children can be divided into groups of 2 and 3, we can use combinatorics. The number of ways to choose 2 children out of 9 is given by the combination formula C(9, 2), and the number of ways to choose 3 children out of the remaining 7 is given by C(7, 3). Therefore, the total number of ways is C(9, 2) × C(7, 3). Using a calculator or the formula C(n, r) = n! / (r! × (n-r)!), we find that C(9, 2) = 36 and C(7, 3) = 35. Multiplying these together gives us 36 × 35 = 126 ways.
To calculate the number of ways in which 9 children can be divided into groups of 3 and 4, we can use similar combinatorics. The number of ways to choose 3 children out of 9 is given by C(9, 3), and the number of ways to choose 4 children out of the remaining 6 is given by C(6, 4). Therefore, the total number of ways is C(9, 3) × C(6, 4). Using the combination formula, we find that C(9, 3) = 84 and C(6, 4) = 15. Multiplying these together gives us 84 × 15 = 1260 ways.
To calculate the number of ways in which 9 children can be divided into groups of 2, 3, and 4, we need to find the intersection of the sets of ways from the previous two scenarios. This can be done by multiplying the number of ways from the first scenario (126) by the number of ways from the second scenario (1260). Therefore, the total number of ways is 126 × 1260 = 158760 ways.
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