Choose 2 juniors and 2 seniors.
There are seven positions to be filled.
The first position can be filled using any of the 7 letters contained in PROBLEM.
The second position can be filled by the remaining 6 letters as the letters should not repeat.
The third position can be filled by the remaining 5 letters only and so on.
Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! ways.
ABACUS is a 6 letter word with 3 of the letters being vowels.
If the 3 vowels have to appear together, then there will 3 other consonants and a set of 3 vowels together.
These 4 elements can be rearranged in 4! Ways.
The 3 vowels can rearrange amongst themselves in 3!/2! ways as "a" appears twice.
Hence, the total number of rearrangements in which the vowels appear together are (4! x 3!)/2!
If a card hand that consists of four Queens and an Ace is rearranged, nothing has changed.
The hand still contains four Queens and an Ace. Thus, use the combination formula for problems with cards.
We have 4 eights and 4 sevens.
We want 3 eights and 2 sevens.
C(have 4 eights, want 3 eights) x C(have 4 sevens, want 2 sevens)
C(4,3) x C(4,2) = 24
Therefore there are 24 different ways in which to deal the desired hand.
Since order does not matter, use the combination formula
= 24/6 = 4
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is = 495.
Therefore, we can draw 495 quadrilaterals
The total possible cases would be a 5 card hand with no restrictions : 5
The unwanted cases are:
no queens(out of 48 non-queens cards we get 5)
only 1 queen(out of 4 queens we get 1,and out of 48 non-queens we get 4)
Therefore,
If Jason is on th ecouncil,this reduces the selction pool to only 13 people,out of which we still need to select 4.
So, = 715
First we need to choose two vowels and then three consonants . Now that we have 5 letters required to make the word,arrange them in 5! ways.
So,
There are ways of selecting two men, and ways of selecting a woman.Since each position in the committee is different,arrange the three people in 3! ways.
So,
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