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Permutations Combinations 1-2


11In how many ways can the letters of the word 'BEAUTY' be arranged so that the words always start with $A$ and does not ends with $B$?
A96
B78
C40
D36


12In how many ways can the letters of the word 'BEAUTY' be arranged so that the vowels are always together?
A112
B128
C144
D172


13

How many different words with or without meaning can be formed using all the letters of the word 'GORGEOUS'?

A$8!$
B$15400$
C$10080$
D$\dfrac{{8!}}{{2!}}$


14

From a group of 12 persons, in how many ways can a selection of 5 persons be made?

A1280
B625
C680
D792


15

From a group of 12 persons, in how many ways can a selection of 5 persons be made such that, A particular person is always included?

A150
B225
C250
D330


16

From a group of 12 persons, in how many ways can a selection of 5 persons be made such that, A particular person is always excluded?

A410
B460
C462
D450


17

From 8 Americans and 5 Chinese , a committee of 6 is to be formed. In how many ways can it be done, If the committee consists exactly 3 chinese?

A560
B640
C582
D552


18

From 8 Americans and 5 Chinese , a committee of 6 is to be formed. In how many ways can it be done, If the committee consist at least 3 Americans?

A1544
B1654
C1568
D1854


19City P is connected to city Q with 5 diffrent highways and city Q is connected to City R with 8 different highways.In how many ways one can choose a different route to travel from P to R via city Q.
A30
B50
C40
D70


208 girls are to be made to stand in a row for a photograph. Among them three particular girls want to be together. In how many ways they can be arranged?
A$6! \times 3!$
B$5! \times 3!$
C$8! - 3!$
D$8! - 3! + 1$