HelloPlease help me with these 3 questions Thanks a lot!!! 1. (i) (2 points) How many ways can one arrange the letters of the word DECEMBER?(ii) (3 points) How many of the arrangements in part (i) contain the word EMBER?(iii) (5 points) How many of the arrangements in part (i) have at least four consonants in a row?(Vowels are A, E, I, O and U. Consonants are letters that are not vowels.)2. You are planning a wedding, and there are 10 people participating in the wedding ceremony.(i) (3 points) During the ceremony, the 10 participants will walk down the aisle in pairs (groups of2), one pair at a time. How many ways can the 10 participants walk down the aisle in pairs if itmatters which person is on the left of the aisle, and which is on the right?(ii) (3 points) After walking down the aisle and completing the wedding ceremony, the 10 participantswill leave the ceremony in pairs. How many ways can the 10 participants leave the ceremony inpairs, one pair at a time, if the left and right orientation of each pair is now irrelevant?(iii) (4 points) After leaving the ceremony there is a reception held where the 10 wedding participantswill dance together. How many ways can the 10 participants form pairs while dancing at the sametime?3. Suppose you have two fair dice, each with 6 faces.• One die is coloured blue and has the following faces: {1, 1,1, 2, 2, 3}.• The other die is coloured red, and has the following faces {1,1, 2, 2, 3, 3}.You run an experiment where you throw each die once and record the results.(i) (3 points) Explicitly write out the sample space S for this experiment. If pB is the probabilitydistribution for the blue die and pR is the probability distribution for the red die, write out theprobability distributions.(ii) (3 points) Let E be the event "The blue die is odd and the red die is even." Write out E andcompute P(E).(iii) (3 points) Let F be the event “the sum of the dice is 5." Write out F and compute P(F). Are Eand F mutually exclusive?(iv) (1 point) Give an example of an event G such that G C S and G is mutually exclusive to both Eand F.

As per the company rule, we are supposed to do only one problem. Kindly repost the remaining…

1. (i) (2 points) How many ways can one arrange the letters of the word DECEMBER? (ii) (3 points) How many of the arrangements in part (i) contain the word EMBER? (iii) (5 points) How many of the arrangements in part (i) have at least four consonants in a row? (Vowels are A, E, I, O and U. Consonants are letters that are not vowels.)