To distribute candies to at least k children, we need to distribute a minimum of k candies. This ensures that each child receives at least one candy. If the candies are indistinguishable, we can distribute any number of candies equal to or greater than k to ensure that each child receives at least one candy. **

When rolling 2 indistinguishable dice, the number of possible outcomes is 21 because there are 6 possible outcomes for the first die and 6 possible outcomes for the second die, giving a total of 36 possible combinations. However, since the dice are indistinguishable, we need to divide by 2 to account for the duplicate combinations (e.g. (1,2) and (2,1)). This gives us 36/2 = 18 unique combinations. Additionally, there are 3 combinations where both dice show the same number (1-1, 2-2, 3-3, 4-4, 5-5, 6-6), bringing the total number of possible outcomes to 18 + 3 = 21. **

When throwing three indistinguishable dice, the total number of outcomes is 216 (6^3). To find the number of outcomes where no 5 appears, we need to subtract the outcomes where at least one 5 appears from the total. There are 125 outcomes where at least one 5 appears (5^3), so the number of outcomes where no 5 appears is 91 (216 - 125). **

There are several energy drinks on the market that are designed to mimic the taste of Red Bull, such as Monster Energy's "Ultra Red" and Rockstar Energy's "Punched." These drinks often have similar flavor profiles to Red Bull, with a mix of sweetness and tartness. While they may not be identical in taste, they are close enough that some consumers find them practically indistinguishable from regular Red Bull. **

The valves on heating pipes are typically ball valves or gate valves. Ball valves have a spherical disc inside that controls the flow of water by rotating the handle, while gate valves have a gate or wedge that moves up and down to control the flow. Both types of valves are used to regulate the flow of hot water through the heating system and can be manually operated to adjust the temperature or shut off the flow completely. **

Yes, the consumption of energy-saving pumps may increase when replacing heating pipes. This is because energy-saving pumps are designed to operate more efficiently and effectively with newer heating systems and pipes. The improved performance of the energy-saving pumps may lead to increased usage, as they are able to distribute heat more evenly and effectively throughout the system. Additionally, the replacement of old pipes with newer, more efficient ones may also contribute to increased energy consumption, as the system may be able to operate more efficiently overall. **

Some recommended mixers for cocktails include soda water, tonic water, ginger beer, and fruit juices such as orange, cranberry, and pineapple. These mixers can be used to create a wide variety of classic and modern cocktails, and can be easily combined with various spirits to create refreshing and flavorful drinks. Additionally, simple syrup and bitters are also commonly used as mixers to add sweetness and depth of flavor to cocktails. **

Suspension filtration works by passing a mixture of solid particles and liquid through a filter medium. The solid particles are too large to pass through the filter, so they are retained on the surface or within the pores of the filter. The liquid, which is now free of the solid particles, passes through the filter and is collected on the other side. This process separates the solid particles from the liquid, allowing for the purification or concentration of the liquid. **