# 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

A1280
B625
C680
D792

15

A150
B225
C250
D330

16

A410
B460
C462
D450

17

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$8! - 3! + 1$