how many arr. of letters in word SPECIAL have letters SPE together & in order?

Upcoming tutorial quiz coming up nxt week and probability still killing me could anyone please help me with these few Q's, textbook doesnt even display the answer and have spent couple hours already. (Please do note that im not just seeking solutions, i really want to know how to tackle these problems!!!)

1. How many ways can letters of the word SPECIAL be arranged such that the letters SPE appear together and in that order

2. A school has 500 pupils. A pupil who is absent has a probability of 0.2 of returning to school tomorrow. A pupil who is not absent today has a probability of 0.6 of being absent tomorrow. If 324 pupils are absent today, how many will be absent 3 days from now

3. Josh plays a game with three other friends. To win, Josh has to roll the die with a value higher than each his friends'. Josh's friends have values 7, 11 and 2 respectively. If Josh rolls a 20-sided die three times, what is the probability that he wins against all three friends

aanthnnyyy said:

Upcoming tutorial quiz coming up nxt week and probability still killing me

could anyone please help me with these few Q's, textbook doesnt even display the answer and have spent couple hours already. (Please do note that im not just seeking solutions, i really want to know how to tackle these problems!!!)

1. How many ways can letters of the word SPECIAL be arranged such that the letters SPE appear together and in that order

2. A school has 500 pupils. A pupil who is absent has a probability of 0.2 of returning to school tomorrow. A pupil who is not absent today has a probability of 0.6 of being absent tomorrow. If 324 pupils are absent today, how many will be absent 3 days from now

3. Josh plays a game with three other friends. To win, Josh has to roll the die with a value higher than each his friends'. Josh's friends have values 7, 11 and 2 respectively. If Josh rolls a 20-sided die three times, what is the probability that he wins against all three friends

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aanthnnyyy said:

...have spent couple hours already.

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Great! What are your thoughts? What have you tried? Where are you getting stuck?

aanthnnyyy said:

1. How many ways can letters of the word SPECIAL be arranged such that the letters SPE appear together and in that order

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You have been given the "letters" C, I, A, L, and SPE. In how many ways may these be arranged? (Use the formula they gave you for this.)

aanthnnyyy said:

2. A school has 500 pupils. A pupil who is absent has a probability of 0.2 of returning to school tomorrow. A pupil who is not absent today has a probability of 0.6 of being absent tomorrow. If 324 pupils are absent today, how many will be absent
3 days from now

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Hint: Markov process.

aanthnnyyy said:

3. Josh plays a game with three other friends. To win, Josh has to roll the die with a value higher than each his friends'. Josh's friends have values 7, 11 and 2 respectively. If Josh rolls a 20-sided die three times, what is the probability that he wins against all three friends?

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Does he roll against them in order?

Thank you!