Question:easy

A four-digit number is formed by using only the digits 1, 2 and 3 such that both 2 and 3 appear at least once. The number of all such four-digit numbers is

Updated On: Jan 15, 2026
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Solution and Explanation

Scenario I: The digits are \(2, 2, 2, 3.\) Total arrangements: \( \frac {4!}{3!} = 4 \)

Scenario II: The digits are \(2, 2, 3, 3.\) Total arrangements: \( \frac {4!}{2!.2!} = 6 \)

Scenario III: The digits are \(2, 3, 3, 3.\) Total arrangements: \( \frac {4!}{3!} = 4 \)

Scenario IV: The digits are \(2, 3, 3, 1.\) Total arrangements: \( \frac {4!}{2!} = 12 \)

Scenario V: The digits are \(2, 2, 3, 1.\) Total arrangements: \( \frac {4!}{2!} = 12 \)

Scenario VI: The digits are \(2, 3, 1, 1.\) Total arrangements: \( \frac {4!}{2!} = 12 \)

Therefore, the total number of possible arrangements is \( 12+12+12+4+6+4 = 50 \).

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
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