Soal Kuis Materi Kaidah Pencacahan

Ali memiliki 2 sepatu dan 3 kaos kaki. Untuk setiap sepatu, Ali dapat memilih salah satu dari 3 kaos kaki yang berbeda. Oleh karena itu, banyak cara Ali memakai sepatu dan kaos kaki ke sekolah adalah 2 x 3 = 6.

The question asks for the number of possible combinations that can be formed using the numbers 1, 2, 3, 4, 5, and 6, where no number can be repeated. Looking at the given options, it can be observed that the numbers are arranged in ascending order. Therefore, the correct answer is the second option, 120, as it is the next number in the ascending order sequence.

There are 5 choices for the first digit, 5 choices for the second digit, and 5 choices for the third digit. Therefore, the total number of possible 3-digit numbers is 5 x 5 x 5 = 125.

There are six children sitting around a circular table. The number of ways they can sit is determined by the number of arrangements possible for six objects in a circle. The formula to calculate the number of arrangements of n objects in a circle is (n-1)!. Therefore, the number of ways the children can sit is (6-1)! = 5! = 5x4x3x2x1 = 120. However, since the table is circular, each arrangement can be rotated, resulting in the same configuration. Therefore, we divide the total number of arrangements by the number of objects to get the number of unique arrangements, which is 120/6 = 20.

The number of possible arrangements for the class committee can be calculated using the formula for permutations. Since there are 34 students in the class and 3 positions to be filled (chairperson, secretary, treasurer), the number of possible arrangements is 34P3. This can be calculated as 34! / (34-3)! = 34! / 31! = 34 x 33 x 32 = 35,904. Therefore, the correct answer is 35.904.

The word "NANAS" has 5 letters. To find the number of arrangements, we can use the formula for permutations of a set with repeated elements, which is n!/a!b!c!..., where n is the total number of elements and a, b, c, etc. are the counts of each repeated element. In this case, there are 2 "N" letters, so we have 5!/2! = 5x4x3x2x1 / 2x1 = 60/2 = 30 possible arrangements.

The number of handshakes that can occur in a meeting with 10 people who do not know each other can be calculated using the formula n(n-1)/2, where n is the number of people. In this case, n=10, so the formula becomes 10(10-1)/2 = 10(9)/2 = 90/2 = 45. Therefore, there would be 45 handshakes in the meeting.

Pak Ahmad memiliki 3 mobil dan 4 sepeda motor yang digunakan untuk pergi ke kantor. Jumlah total kendaraan yang dimiliki adalah 7, sehingga banyak cara Pak Ahmad pergi ke kantor adalah 7.

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There are a total of 11 balls in the box, and we need to find the number of ways to choose 2 green balls. Since there are only 5 green balls in the box, we cannot choose 2 green balls at the same time. Therefore, the correct answer is 10.