Discussion

Explanation:

Here letters are distinct, but the letter boxes are similar.

Now, we first need to do the grouping of letters i.e.,

              LB      LB    LB
Case 1    4        0       0
Case 2    3        1       0
Case 3    2        1       1
Case 4    2         2      0

Case 1: Since all 4 letters go in a single letter box, there is only 1 way of doing this.

Case 2: 3 letters go in one of the letter boxes and 1 letter goes in another letter box. 

Number of ways of selecting 3 letters out of 4 = ⁴C₃ = 4 ways. We send these 3 letters in any of the boxes (they are all similar) in 1 way. The 4^th letter can be sent in any of the remaining two letter boxes (similar) in 1 way.

∴ Total number of ways = 4 × 1 × 1 = 4 ways.

Case 3: 2 letters go in one of the letter boxes and 2 other go in different letter boxes. 

Number of ways of selecting 2 letters out of 4 = ⁴C₂ = 6 ways. We send these 2 letters in any of the boxes (they are all similar) in 1 way. The 3^rd and the 4^th letter each can be sent in the remaining two letter boxes (similar) in 1 way.

∴ Total number of ways = 6 × 1 × 1 = 6 ways.

Case 4: 2 letters go in on of the letter boxes and 2 others go in another letter box.

Number of ways of making 2 groups of 2 letters each = 3.

L₁L₂ & L₃L₄ or L₁L₃ & L₂L₄ or L₁L₄ & L₂L₃.

∴ The required answer = 1 + 4 + 6 + 3 = 14 ways.

Hence, 14.

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