Answer to Question #129673 in Discrete Mathematics for Gazal

Question

How many ways can be letters { 5.a. 4.b, 1.c} be arranged so that all letters of

same kind are in a single block

Answer 1

Number of ways of selecting 3 different letters

$=3C_3 = 1$

Number of ways to select 1 similar and 2 different letter:

$=2C_1\times 2C_2 = 2$

Number of ways of selecting 1 similar + 1 more similar letter and 1 different letter:

$=2C_2\times 1C_1 = 1$

Number of ways to select 2 similar and 1 different letter:

$=2C_2\times 2C_1 = 2$

ways of selecting 3 similar letters:

$=$ 1

total ways:  $=1+2+1+2+1 =7$