A dice is rolled 4 times,the numbers appearing are listed. The number of different throws, such that the largest number appearing in the list is not 4, is:

The question asks for the number of outcomes where the largest number rolled in 4 attempts is not 4. This means the largest number must be 1, 2, or 3. The number of different throws possible using only the numbers 1, 2, and 3 is 3^4, which equals 81. However, if the list of options implies a question about outcomes that include the number 4 but do not have 4 as the largest (meaning a 5 or 6 is also rolled), we calculate total outcomes of 6^4 (1296), minus outcomes with only 1, 2, 3, 4, which is 4^4 (256), minus outcomes with only 1, 2, 3 (81), leaving 959. Re-evaluing the interpretation for a sum or specific condition is needed, but if calculating throws where the maximum is strictly greater than 4, there are 2^4 (16) outcomes of only 5 and 6, making the correct calculation for outcomes where the maximum is exactly 4 calculated as 4^4 - 3^4 = 175. Thus, there are 175 different throws where the largest number appearing is exactly 4.

• Thanks
• Wrong explanation