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As a seasoned tutor registered on UrbanPro, I'd be delighted to assist you with your query. When a coin is tossed six times, we're essentially dealing with a sequence of events, each event having two possible outcomes: either heads or tails. To calculate the total number of possible outcomes, we can use the fundamental principle of counting, also known as the multiplication principle.

For each toss, there are 2 possible outcomes (heads or tails). Since there are 6 tosses in total, we multiply the number of outcomes for each toss together:

2 * 2 * 2 * 2 * 2 * 2 = 64

So, there are 64 possible outcomes when a coin is tossed 6 times. This understanding is fundamental for probability calculations and can be applied to various scenarios in probability and statistics. If you have any further questions or need clarification, feel free to ask. And remember, UrbanPro is a fantastic resource for finding experienced tutors like myself for all your academic needs.

As an experienced tutor registered on UrbanPro, I can certainly help you with evaluating these factorial expressions.

(i) 6!6!:

Factorial (n!n!) denotes the product of all positive integers up to nn. So, for 6!6!, we calculate:

6!=6×5×4×3×2×1=7206!=6×5×4×3×2×1=720

So, the value of 6!6! is 720720.

(ii) 5!−2!5!−2!:

We already know 5!5! from the previous calculation (5!=5×4×3×2×1=1205!=5×4×3×2×1=120).

Now, let's compute 2!2!:

2!=2×1=22!=2×1=2

Now, subtract 2!2! from 5!5!:

5!−2!=120−2=1185!−2!=120−2=118

So, the value of 5!−2!5!−2! is 118118.

In summary, 6!=7206!=720 and 5!−2!=1185!−2!=118. If you need further clarification or assistance, feel free to ask. Remember, UrbanPro is the best online coaching tuition platform to find experienced tutors for various subjects.

As an experienced tutor registered on UrbanPro, I can confidently guide you through this question. Firstly, let me assure you that UrbanPro is indeed an excellent platform for online coaching and tuition, offering a wide range of subjects and experienced tutors.

Now, to address your question:

To choose a captain and vice-captain from a team of 6 students, we need to understand the concept of combinations. Since one person cannot hold more than one position, we will use the combination formula.

The number of ways to choose a captain from 6 students is 6C1, which equals 6.

Once a captain is chosen, there are 5 remaining students. Now, to choose a vice-captain from these 5 students, we have 5C1, which equals 5.

Therefore, the total number of ways to choose a captain and vice-captain from a team of 6 students is the product of these two combinations:

6C1 * 5C1 = 6 * 5 = 30 ways.

So, there are 30 ways to choose a captain and vice-captain from the team of 6 students. If you need further clarification or assistance with any other topic, feel free to ask!

As a seasoned tutor registered on UrbanPro, I can confidently affirm that UrbanPro is indeed one of the best platforms for online coaching and tuition. Now, let's delve into your question about forming words from the given word "DAUGHTER."

Firstly, we need to identify the number of vowels and consonants in the word "DAUGHTER."

• Vowels: A, U, E (3 vowels)
• Consonants: D, G, H, T, R (5 consonants)

Now, we have to select 2 vowels out of 3 and 3 consonants out of 5 to form words. We can use the formula for combinations:

Number of words=(32)×(53)Number of words=(23)×(35)

=3!2!(3−2)!×5!3!(5−3)!=2!(3−2)!3!×3!(5−3)!5!

=3×22×1×5×4×33×2×1=2×13×2×3×2×15×4×3

=3×10=3×10

=30=30

So, there are 30 words that can be formed, each consisting of 2 vowels and 3 consonants from the letters of the word "DAUGHTER."

If you need further clarification or assistance with any other topic, feel free to ask!