Stanry

124 Questions
12 Answers

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Math

Bekah has three brass house number digits: 2, 3, 4, 5, and 6. How many distinct numbers can she form using one or more of the digits, if her number must be divisible by 4?

Stanry 5 hours ago

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19

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Counting

The following cards are split into four piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
The cards are:
Ace of clubs
Ace of diamonds прочитайте больше ..

Stanry 17 апр. 2025 г.

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11

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Counting

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

Stanry 16 апр. 2025 г.

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5

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Counting

How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?

Stanry 16 апр. 2025 г.

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12

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Counting

How many 7-digit sequences have a digit that appears at least 6 times?
(For example, 3339333 and 0200000 are two such sequences. A sequence is allowed to begin with 0.)

Stanry 15 апр. 2025 г.

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15

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Counting

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

Stanry 15 апр. 2025 г.

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16

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Counting

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 5?

Stanry 14 апр. 2025 г.

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22

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Counting

How many subsets of \{0, 1, \dots, 9\} have the property that there are at least two elements and the sum of the two largest elements is 4?

Stanry 14 апр. 2025 г.

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16

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Counting

A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3) is a permutation of (1,2,3,4,5).
Find the number of permutations (x_1, x_2, \dots, x_8) прочитайте больше ..

Stanry 13 апр. 2025 г.

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13

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Counting

Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.

Stanry 13 апр. 2025 г.

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19

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Counting

A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.
You are dealt a hand of прочитайте больше ..

Stanry 13 апр. 2025 г.

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12

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Counting

In the array below, in how many different ways can we start with the letter and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCS"?
A прочитайте больше ..

Stanry 13 апр. 2025 г.

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20

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Counting

How many squares in the plane have at least two points in the lattice below as vertices?

Stanry 13 апр. 2025 г.

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3

5

2

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Counting

At a meeting, two scientists, two mathematicians, two historians, and two artists are to be seated around a circular table. In how many ways can they be seated so that all four pairs of people from the same discipline are seated together?

Stanry 12 апр. 2025 г.

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The number of ways is 10*9 = 90.

Stanry1 окт. 2024 г.